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1
8022 (EampM) -Lecture 1
Gabriella Sciolla
Topics How is 8022 organized Brief math recap Introduction to Electrostatics
2
Welcome to 8022
8022 advanced electricity and magnetism for freshmen or electricity and magnetism for advanced freshmen
Advanced
Both integral and differential formulation of EampM
Goal look at Maxwellrsquos equations
hellip and be able to tell what they really mean Familiar with math and very interested in physics Fun class but pretty hard 8022 or 802T
September 8 2004 8022 ndash Lecture 1
3
8022 web page Bookmarkhellip
hellipand watch out for typos
Everything You Always Wanted to Know About 8022 But Were Afraid to Ask
httpwebmitedu8022www
September 8 2004 8022 ndash Lecture 1
4
Staff and Meetings
September 8 2004 8022 ndash Lecture 1
5
Textbook
E M Purcell Electricity and Magnetism Volume 2 -Second edition
Advantages 1048708 Bible for introductory EampM for generations of physicists
Disadvantage 1048708 cgs units
September 8 2004 8022 ndash Lecture 1
6
Problem sets
Posted on the 8022 web page on Thu night and due on Thu at 430 PM of the following week Leave them in the 8022 lockbox at PEO
Exceptions Pset 0 (Math assessment) due on Monday Sep 13 Pset 1 (Electrostatiscs) due on Friday Sep 17
How to work on psets Try to solve them by yourself first Discuss problems with friends and study group Write your own solution
September 8 2004 8022 ndash Lecture 1
7
Grades
How do we grade 8022
Homeworks and Recitations (25)
Two quizzes (20 each)
Final (35)
Laboratory (2 out of 3 needed to pass)
More info on exams
Two in-class (26-100) quiz during normal class hours
Tuesday October 5 (Quiz 1)
Tuesday November 9 (Quiz 2)
Final exam
Tuesday December 14 (9 AM -12 Noon) location TBD
All grades are available online through the 8022 web page
September 8 2004 8022 ndash Lecture 1
NB You may not pass the course without completing the laboratories
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
2
Welcome to 8022
8022 advanced electricity and magnetism for freshmen or electricity and magnetism for advanced freshmen
Advanced
Both integral and differential formulation of EampM
Goal look at Maxwellrsquos equations
hellip and be able to tell what they really mean Familiar with math and very interested in physics Fun class but pretty hard 8022 or 802T
September 8 2004 8022 ndash Lecture 1
3
8022 web page Bookmarkhellip
hellipand watch out for typos
Everything You Always Wanted to Know About 8022 But Were Afraid to Ask
httpwebmitedu8022www
September 8 2004 8022 ndash Lecture 1
4
Staff and Meetings
September 8 2004 8022 ndash Lecture 1
5
Textbook
E M Purcell Electricity and Magnetism Volume 2 -Second edition
Advantages 1048708 Bible for introductory EampM for generations of physicists
Disadvantage 1048708 cgs units
September 8 2004 8022 ndash Lecture 1
6
Problem sets
Posted on the 8022 web page on Thu night and due on Thu at 430 PM of the following week Leave them in the 8022 lockbox at PEO
Exceptions Pset 0 (Math assessment) due on Monday Sep 13 Pset 1 (Electrostatiscs) due on Friday Sep 17
How to work on psets Try to solve them by yourself first Discuss problems with friends and study group Write your own solution
September 8 2004 8022 ndash Lecture 1
7
Grades
How do we grade 8022
Homeworks and Recitations (25)
Two quizzes (20 each)
Final (35)
Laboratory (2 out of 3 needed to pass)
More info on exams
Two in-class (26-100) quiz during normal class hours
Tuesday October 5 (Quiz 1)
Tuesday November 9 (Quiz 2)
Final exam
Tuesday December 14 (9 AM -12 Noon) location TBD
All grades are available online through the 8022 web page
September 8 2004 8022 ndash Lecture 1
NB You may not pass the course without completing the laboratories
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
3
8022 web page Bookmarkhellip
hellipand watch out for typos
Everything You Always Wanted to Know About 8022 But Were Afraid to Ask
httpwebmitedu8022www
September 8 2004 8022 ndash Lecture 1
4
Staff and Meetings
September 8 2004 8022 ndash Lecture 1
5
Textbook
E M Purcell Electricity and Magnetism Volume 2 -Second edition
Advantages 1048708 Bible for introductory EampM for generations of physicists
Disadvantage 1048708 cgs units
September 8 2004 8022 ndash Lecture 1
6
Problem sets
Posted on the 8022 web page on Thu night and due on Thu at 430 PM of the following week Leave them in the 8022 lockbox at PEO
Exceptions Pset 0 (Math assessment) due on Monday Sep 13 Pset 1 (Electrostatiscs) due on Friday Sep 17
How to work on psets Try to solve them by yourself first Discuss problems with friends and study group Write your own solution
September 8 2004 8022 ndash Lecture 1
7
Grades
How do we grade 8022
Homeworks and Recitations (25)
Two quizzes (20 each)
Final (35)
Laboratory (2 out of 3 needed to pass)
More info on exams
Two in-class (26-100) quiz during normal class hours
Tuesday October 5 (Quiz 1)
Tuesday November 9 (Quiz 2)
Final exam
Tuesday December 14 (9 AM -12 Noon) location TBD
All grades are available online through the 8022 web page
September 8 2004 8022 ndash Lecture 1
NB You may not pass the course without completing the laboratories
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
4
Staff and Meetings
September 8 2004 8022 ndash Lecture 1
5
Textbook
E M Purcell Electricity and Magnetism Volume 2 -Second edition
Advantages 1048708 Bible for introductory EampM for generations of physicists
Disadvantage 1048708 cgs units
September 8 2004 8022 ndash Lecture 1
6
Problem sets
Posted on the 8022 web page on Thu night and due on Thu at 430 PM of the following week Leave them in the 8022 lockbox at PEO
Exceptions Pset 0 (Math assessment) due on Monday Sep 13 Pset 1 (Electrostatiscs) due on Friday Sep 17
How to work on psets Try to solve them by yourself first Discuss problems with friends and study group Write your own solution
September 8 2004 8022 ndash Lecture 1
7
Grades
How do we grade 8022
Homeworks and Recitations (25)
Two quizzes (20 each)
Final (35)
Laboratory (2 out of 3 needed to pass)
More info on exams
Two in-class (26-100) quiz during normal class hours
Tuesday October 5 (Quiz 1)
Tuesday November 9 (Quiz 2)
Final exam
Tuesday December 14 (9 AM -12 Noon) location TBD
All grades are available online through the 8022 web page
September 8 2004 8022 ndash Lecture 1
NB You may not pass the course without completing the laboratories
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
5
Textbook
E M Purcell Electricity and Magnetism Volume 2 -Second edition
Advantages 1048708 Bible for introductory EampM for generations of physicists
Disadvantage 1048708 cgs units
September 8 2004 8022 ndash Lecture 1
6
Problem sets
Posted on the 8022 web page on Thu night and due on Thu at 430 PM of the following week Leave them in the 8022 lockbox at PEO
Exceptions Pset 0 (Math assessment) due on Monday Sep 13 Pset 1 (Electrostatiscs) due on Friday Sep 17
How to work on psets Try to solve them by yourself first Discuss problems with friends and study group Write your own solution
September 8 2004 8022 ndash Lecture 1
7
Grades
How do we grade 8022
Homeworks and Recitations (25)
Two quizzes (20 each)
Final (35)
Laboratory (2 out of 3 needed to pass)
More info on exams
Two in-class (26-100) quiz during normal class hours
Tuesday October 5 (Quiz 1)
Tuesday November 9 (Quiz 2)
Final exam
Tuesday December 14 (9 AM -12 Noon) location TBD
All grades are available online through the 8022 web page
September 8 2004 8022 ndash Lecture 1
NB You may not pass the course without completing the laboratories
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
6
Problem sets
Posted on the 8022 web page on Thu night and due on Thu at 430 PM of the following week Leave them in the 8022 lockbox at PEO
Exceptions Pset 0 (Math assessment) due on Monday Sep 13 Pset 1 (Electrostatiscs) due on Friday Sep 17
How to work on psets Try to solve them by yourself first Discuss problems with friends and study group Write your own solution
September 8 2004 8022 ndash Lecture 1
7
Grades
How do we grade 8022
Homeworks and Recitations (25)
Two quizzes (20 each)
Final (35)
Laboratory (2 out of 3 needed to pass)
More info on exams
Two in-class (26-100) quiz during normal class hours
Tuesday October 5 (Quiz 1)
Tuesday November 9 (Quiz 2)
Final exam
Tuesday December 14 (9 AM -12 Noon) location TBD
All grades are available online through the 8022 web page
September 8 2004 8022 ndash Lecture 1
NB You may not pass the course without completing the laboratories
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
7
Grades
How do we grade 8022
Homeworks and Recitations (25)
Two quizzes (20 each)
Final (35)
Laboratory (2 out of 3 needed to pass)
More info on exams
Two in-class (26-100) quiz during normal class hours
Tuesday October 5 (Quiz 1)
Tuesday November 9 (Quiz 2)
Final exam
Tuesday December 14 (9 AM -12 Noon) location TBD
All grades are available online through the 8022 web page
September 8 2004 8022 ndash Lecture 1
NB You may not pass the course without completing the laboratories
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
8
hellipLast but not leasthellip
Come and talk to us if you have problems or questions 8022 course material I attended class and sections and read the book but I still donrsquot understand concept xyz and I am stuck on the pset
Math I canrsquot understand how Taylor expansions work or why I should care about themhellip Curriculum is 8022 right for me or should I switch to TEAL
Physics in general Questions about matter-antimatter asymmetry of the Universe elementary constituents of matter (Sciolla) or gravitational waves (Kats) are welcome
September 8 2004 8022 ndash Lecture 1
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
9
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
10
Your best friend in 8022 math
Math is an essential ingredient in 8022 Basic knowledge of multivariable calculus is essential You must be enrolled in 1802 or 18022 (or even more advanced) To be proficient in 8022 you donrsquot need an A+ in 18022 Basic concepts are used
Assumption you are familiar with these concepts already but are a bit rustyhellip
Letrsquos review some basic concepts right now
NB excellent reference D Griffiths Introduction to electrodynamics Chapter 1
September 8 2004 8022 ndash Lecture 1
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
11
Derivative
Given a function f(x) what is itrsquos derivative
The derivative tells us how fast f varies when x varies
The derivative is the proportionality factor between a change in x and a change in f
What if f=f(xyz)
September 8 2004 8022 ndash Lecture 1
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
12
Gradient
Letrsquos define the infinitesimal displacement
Definition of Gradient
Conclusions f measures how fast f(xyz) varies when x y and z vary Logical extension of the concept of derivative f is a scalar function but f is a vector
September 8 2004 8022 ndash Lecture 1
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
13
The ldquodelrdquo operator
Definition
Properties
It looks like a vector It works like a vector But itrsquos not a real vector because itrsquos meaningless by itself Itrsquos an operator
How it works It can act on both scalar and vector functions
Acting on a sca ar function gradient (vector) Acting on a vector function with dot product divergence (scalar) Acting on a sca ar function with cross product curl (vector)
September 8 2004 8022 ndash Lecture 1
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
14
Divergence
Given a vector function
we define its divergence as
Observations
The divergence is a scalar
Geometrical interpretat on it measures how much the function ldquospreads around a pointrdquo
September 8 2004 8022 ndash Lecture 1
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
15
Divergence interpretation
Calculate the divergence for the following functions
September 8 2004 8022 ndash Lecture 1
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
16
Does this remind you of anything
Electric field around a charge has divergence ne 0
div Egt0 for + charge faucet div E lt0 for ndash charge sink
September 8 2004 8022 ndash Lecture 1
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
17
Curl
Given a vector function
we define its curl as
Observations
The curl is a vector Geometrical interpretation it measures how much the function ldquocurls around a pointrdquo
September 8 2004 8022 ndash Lecture 1
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
18
Curl interpretation
Calculate the curl for the following function
This is a vortex non zero curl
September 8 2004 8022 ndash Lecture 1
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
19
Does this sound familiar
Magnetic filed around a wire
September 8 2004 8022 ndash Lecture 1
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
20
An now our feature presentation Electricity and Magnetism
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
21
The electromagnetic force
Ancient historyhellip
500 BC ndash Ancient Greece
Amber ( =ldquoelectronrdquo) attracts light objects Iron rich rocks from (Magnesia) attract iron
1730 -C F du Fay Two flavors of charges
Positive and negative
1766-1786 ndash PriestleyCavendishCoulomb
EM interactions follow an inverse square law
Actual precision better than 2109
1800 ndash Volta
Invention of the electric battery
NB Till now Electricity and Magnetism are disconnected
September 8 2004 8022 ndash Lecture 1
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
22
1820 ndash Oersted and Ampere Established first connection between electricity and magnetism 1831 ndash Faraday Discovery of magnetic induction 1873 ndash Maxwell Maxwellrsquos equations The birth of modern Electro-Magnetism 1887 ndash Hertz Established connection between EM and radiation 1905 ndash Einstein
Special relativity makes connection between Electricity and Magnetism as natural as it can be
The electromagnetic force
hellipHistoryhellip (cont)
September 8 2004 8022 ndash Lecture 1
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
23
The electromagnetic force
Modern Physics
The Standard Model of Particle Physics Elementary constituents 6 quarks and 6 leptons
Four elementary forces mediated by 5 bosons
Interaction Mediator Relative Strength Range (cm)
Strong Gluon 1037 10-13
Electromagnetic Photon 1035 Infinite
Weak W+- Z0 1024 10-15
Gravity Graviton 1 Infinite
September 8 2004 8022 ndash Lecture 1
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
24
The electric charge
The EM force acts on charges 2 flavors positive and negative Positive obtained rubbing glass with silk Negative obtained rubbing resin with fur
Electric charge is quantized (Millikan)
Multiples of the e = elementary charge
Electric charge is conserved
In any isolated system the total charge cannot change
If the total charge of a system changes then it means the system is not isolated and charges came in or escaped
September 8 2004 8022 ndash Lecture 1
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
25
Coulombrsquos law
Where
is the force that the charge q feels due to is the unit vector going from to
Consequences
Newtonrsquos third law Like signs repel opposite signs attract
September 8 2004 8022 ndash Lecture 1
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
26
Units cgs vs SI
Units in cgs and SI (Sisteme Internationale)
In cgs the esu is defined so that k=1 in Coulombrsquos law
In SI the Ampere is a fundamental constant
is the permittivity of free space
Length
Time
Current
Mass
Charge electrostatic units (esu) Coulomb(c)
Ampere(A)
September 8 2004 8022 ndash Lecture 1
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
27
Practical info cgs -SI conversion table
FAQ why do we use cgs
Honest answer because Purcell doeshellip
September 8 2004 8022 ndash Lecture 1
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
28
The superposition principle discrete charges
The force on the charge Q due to all the other charges is equal to the vector sum of the forces created by the individual charges
September 8 2004 8022 ndash Lecture 1
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
29
The superposition principle continuous distribution of charges
What happens when the distribution of charges is continuous
Take the limit for integral
where ρ = charge per unit volume ldquovolume charge densityrdquo
September 8 2004 8022 ndash Lecture 1
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
30
The superposition principle
continuous distribution of charges (cont)
1048708 Charges are distributed inside a volume V
Charges are distributed on a surface A
Charges are distributed on a line L
Where
ρ = charge per un t vo ume ldquovo ume charge dens tyrdquo
σ = charge per un t area ldquosurface charge dens tyrdquo
λ = charge per un ength ldquo ne charge dens tyrdquo
September 8 2004 8022 ndash Lecture 1
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
31
Application charged rod
P A rod of length L has a charge Q uniformly spread over t A test charge q is positioned at a distance a from the rodrsquos midpoint Q What is the force F that the rod exerts on the charge q
Answer
September 8 2004 8022 ndash Lecture 1
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
32
Solution charged rod
Look at the symmetry of the problem and choose appropr ate coordinate system rod on x axis symmetric wrt x=0 a on y axis
1048708 Symmetry of the problem F y axis define λ=QL linear charge density
1048708 Trigonometric relations xa=tg a=r
1048708 Consider the infinitesimal charge dFy produced by the element dx
1048708 Now integrate between ndashL2 and L2
September 8 2004 8022 ndash Lecture 1
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
33
Infinite rod Taylor expansion
Q What if the rod length is infinite P What does ldquoinfiniterdquo mean For al practical purposes infinite means gtgt than the other distances in the problem Lgtgta Letrsquos look at the solution
Tay or expand using (2aL) as expansion coefficient remembering that
September 8 2004 8022 ndash Lecture 1
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
34
Rusty about Taylor expansions
Here are some useful remindershellip
September 8 2004 8022 ndash Lecture 1
Exponential function and natural logarithm
Geometric series
Trigonometric functions
