ELECTROMAGNETISM

Four kinds of fundamental forces or interactions:

gravitational interaction

electromagnetic interaction

strong interaction

weak interaction

Evolution of knowledge on electromagnetism

Magnetic phenomena , 2000 BC, China.

Electric and magnetic phenomena , 700 BC, Greece.

Electricity and magnetism are related phenomena, early part of 19th century: Oersted

experiment (1819) and Faraday experiment (1831); Maxwell's theory of

electromagnetism (1873).

The role of electromagnetism

The laws of electricity and magnetism play a central role in the operation of such

devices as MP3 players, mobile phone, televisions, electric motors, computers, high-

energy accelerators, and other electronic devices.

More fundamentally, the interatomic and intermolecular forces responsible for the

formation of materials, solids and liquids, are electric in origin.

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1. Young and Freedman,

Sears and Zemansky's UNIVERSITY PHYSICS

with Modern Physics

12th Edition, Pearson-Addison Wesley.

2. Serway and Jewett,

PHYSICS for Scientists and Engineers

with Modern Physics

7th Edition, Thomson-Brooks/Cole.

3. Halliday and Resnick,

Fundamentals of PHYSICS

9th Edition, Jearl Walker.

2

31. Electric charge and electric field

2. Electric potential and electric energy

3. Electric current; DC circuits

4. Magnetism

5. Electromagnetic induction

6. Maxwells equations.

Chapter 1 Electric charge and electric field

1.1 Electric charge

Plastic rod rubbed on fur, glass rod rubbed with silk are charged.

Charged glass rods repel each other. Charged glass rod attracts charged plastic rod.

Charged plastic rod and fur attract each other.

Two types of electric charge: positive and negative.

Two positive charges or two negative charges repel each other. A positive charge

and a negative charge attract each other.

1.1

4Young p. 710

The structure of an atom can be

described in terms of electrons,

protons, neutrons. Negatively

charged electrons are held within

the atom by attractive electric

forces exerted on them by the

positively charged nucleus. The

protons and neutrons are held

within the stable atomic nuclei by

an attractive interaction, called the

strong nuclear force, that

overcomes the electric repulsion of

the protons.

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Electric charge

and the structure of matter

The magnitude of the charge is the same in electrons and protons.

A neutral atom has as many electrons as protons. The number of protons is called the

atomic number of the element. An atom which gains or loses electron becomes an ion.

Normally, a macroscopic body is neutral and has net charge equal to zero. In most

cases, in order to give an excess charge to a body, we add or remove negatively

charged and highly mobile electrons.

1.3

6

Electric charge is conserved

The principle of conservation of charge:

The algebraic sum of all the electric charges in any closed system is constant.

7

Conservation of charge is thought to be a universal conservation law. No experimental

evidence for any violation of this principle has ever been observed.

The magnitude of charge of the electron or proton is a natural unit of charge

Electric charge is quantized.

The charge of a proton or an electron is called the elementary charge. The charge on

any macroscopic body is always either zero or an integer multiple (negative or

positive) of the elementary charge .

1.2 Conductors, insulators and

induced charges

Materials that permit electric charge to move easily

from one region of the material to another are

conductors.

Materials that do not permit electric charge to move

from one region of the material to another are

insulators.

Most metals are good conductors, while most

nonmetals are insulators.

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Charging by induction

9

Electric Forces on Uncharged Objects

10

11

1.7

Applications of the electric force

Electrostatic painting

Laser printer

Young p.716

1.3 Coulomb's law

12Young p. 716

Coulomb experiment: ;

Coulomb's law:

The magnitude of the electric force between two point charges is directly

proportional to the product of the charges and inversely proportional to the

square of the distance between them.

13

2

1F

r 1 2F q q

1 2

2

q qF k

r

1 22

q qk

rr

rF

Fundamental electric constants

k = 8.987551787 109 N.m2 /C2 8.988 109 N.m2 /C2

or k = (107 N. s2/C2)c2 with c = 2.99792458 108 m/s.

k=1/40 where 0 = 8.854 10-12 C2 /Nm2

9

0

18 988 10

4.k

Nm2/C2 1 2

20

1

4

q q

rr

rF

e= 1.60217653(14)10-19 C

Principle of superposition of forces

Experiments show that when two charges exert forces simultaneously on a third

charge, the total force acting on that charge is the vector sum of the forces that the

two charges would exert individually.

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Example Two equal positive point charges q1 = q2 = 2.0 C are located at x = 0, y =

0.30 m and x = 0, y = - 0.30 m, respectively. What are the magnitude and direction of the

total (net) electric force that these charges exert on a third point charge Q = 4.0 C at

x = 0.40m, y = 0?

Young p. 721

1.4 Electric field and electric forces

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Electric field

We define the electric field at a point as

the electric force experienced by a test

charge q0 at the point, divided by the charge

q0

E

0F

0

0qF

E

If the field at a certain point is known,

then the force experienced by a point

charge q0 placed at that point is

E

0F

0 0qF E

The electric force on a charged body is

exerted by the electric field created by other

charged bodies.

Young 721

+Action-at- a-distance

+Charge on A modifies the space. Charge on

B senses how space has been modified.

Electric field of a point charge

16

00 2

0

1

4

qq

rr

rF

02

0 0

1

4

q

q rr F r

E

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In many cases, especially when studying the electric field in dielectrics, we use the

electric displacement vector or the electric induction vector .

In vacuum,

D

0D E

1.5 Electric field calculations

The superposition of electric fields

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The superposition of electric forces0 1 2 3 0 1 0 2 0 3... ...q q q F F F F E E E

The superposition of electric fields 01 2 3

0

...q

F

E E E E

The principle of superposition of electric fields.

The total electric field at P is the vector sum of the fields at P due to each point

charge in the charge distribution.

Different charge distributions:

linear charge density (C/m)surface charge density (C/m2)volume charge density (C/m3)

Young p.727

Example 1 Point charges q1 and q2 of +12 nC

and -12 nC, respectively, are placed 0.10 m

apart. This combination of two charges with

equal magnitude and opposite sign is called

an electric dipole.

Compute the electric field caused by q1 , the

field caused by q2 , and the total field (a) at

point a; (b) at point b; and (c) at point c.

Young 72819

Example 2 A ring-shaped conductor with

radius a carries a total charge Q uniformly

distributed around it. Find the electric field

at a point P that lies on the axis of the ring at

a distance x from its center.

Linear charge density =Q/2a

3 2

2 20

1

4 /Qx

x a

E i

Symmetry argument.

If x point charge

Example 3 Find the electric field caused by

a disk of radius R with a uniform positive

surface charge density , at a point along theaxis of the disk a distance x from its center.

Assume that x is positive.

In the limit that R>>x, . This is the case of an infinite plane sheet of charge.

20

2 201

12 1/

xE

R x

02E

Example 4 Two infinite plane sheets are

placed parallel to each other, separated by a

distance d. The lower sheet has a uniform

positive surface charge density , and the upper sheet has a uniform negative surface

charge density - with the same magnitude. Find the electric field between the two

sheets, above the upper sheet, and below the

lower sheet.

The electric field between the sheets is a uniform field.

Young p.732

1.6 Electric field lines

Electric field lines can be a big help for visualizing

electric fields and making them seem more real. An

electric field line is an imaginary line or curve drawn

through a region of space so that its tangent at any

point is in the direction of the electric-field vector at

that point.

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The rules for drawing electric field lines:

The lines must begin on a positive charge and termi-

nate on a negative charge. Some lines may begin or end

infinitely far away.

No two field lines can cross.

The number of lines per unit area through a surface

perpendicular to the lines is proportional to the magni-

tude of the electric field in that region. Therefore, the

field lines are close together where the electric field is

strong and far apart where the field is weak.

22Young p. 734

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1.7 Gauss's law

The total number of electric field linespenetrating a surface is called the electric

flux. For a surface that is perpendicular to

the field lines of a uniform field, the electric

flux is .

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1.20E EA

1.21

In the case where the normal to the surface of

area A is at an angle to the uniform electric field, .

Depending on , the flux may be positive or negative.

cosE EA EA

Serway 673

Electric flux

In more general situations, the electric field may

vary over a large surface. We divide the surface

into a large number of small elements, each of

area Ai and define a vector . Then

Summing the contributions of all elements gives an

approximation to the total flux through the surface:

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1.22

i iA A n

cosE i i i i i i iE A A E n E A

E i ii

E A

If the area of each element approaches zero, the

number of elements approaches infinity and the

sum is replaced by an integral.

surface

E d E A

For a closed surface, the normal to the surface, by convention, always point outward.

The net flux through the surface is proportional to the net number of lines leaving the surface, where the net number means the number of lines leaving the surface minus the number of lines entering the surface. We can write

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A closed surface in

an electric field.

The area vectors are,

by convention,

normal to the surface

and point outward.

The flux through an

area element can be

positive (element 1),

zero (element 2), or

negative (element 3).

E nd E dA E A

Gauss's law

The gaussian surface in the shape of a sphere

with a charge q at its center:

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E d EdA E dA E A

2

20 0

14

4E

q qr

r

1.25

The gaussian surfaces with different shape but

surrounding the charge, also:

0E

q

Therefore, the net flux through any closed

surface surrounding a point charge q is

given by q/0 and is independent of the

shape of that surface.

For a point charge located outside the closed surface,

the net flux through the surface is zero.

Therefore, the net electric flux through a closed

surface that surrounds no charge is zero.

In the general cases, where there are many point

charges or there is a continuous distribution of

charge, we use the superposition principle.

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1.26Gauss's law The net flux through a closed surface

equals the algebraic sum of the charges inside the

surface divided by 0

in

0E

qd

E A

Gausss law is an alternative to Coulombs law. It provides a different way to express

the relationship between electric charge and electric field.

Applications of Gauss's law

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Gausss law is useful for determining electric fields when the charge distribution is highly

symmetric. In choosing the gaussian surface, always take advantage of the symmetry of the

charge distribution so that E can be removed from the integral.

1. The value of the electric field can be argued by symmetry to be constant over the portion

of the surface.

2. The dot product can be expressed as a simple algebraic product E dA because and

are parallel.

3. The dot product is zero because and are perpendicular.

4. The electric field is zero over the portion of the surface.

E dA

Example 1 An insulating solid sphere of radius a

has a uniform volume charge density and carries a total positive charge Q

(a) Calculate the magnitude of the electric field at a

point outside the sphere.

(b) Find the magnitude of the electric field at a

point inside the sphere.

E dA

204

QE

r for r>a

03E r

for r

Example 2 Find the electric field a distance r

from a line of positive charge of infinite length

and constant charge per unit length .

Example 3 Find the electric field due to an

infinite plane of positive charge with uniform

surface charge density .

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02E

r

02E

1.8 Charges on conductors

Young p.761, 767 31

If there is an electric field within a conductor,

the field exerts a force on every charge in the

conductor, giving the free charges a net motion.

By definition, an electrostatic situation is one in

which the charges have no net motion. We

conclude that in electrostatics the electric field

at every point within the material of a

conductor must be zero.

Example 1 Two large plane parallel conducting plates are given charges of

equal magnitude and opposite sign; the charge per unit area is + for one and - for theother. Find the electric field in the region between the plates.

Young p. 765, 768 32

Example 2 A solid conductor with a cavity carries a total

charge of +7 nC. Within the cavity, insulated from the

conductor, is a point charge of -5 nC. How much charge

is on each surface (inner and outer) of the conductor?

Testing Gauss's law experimentally

Faraday's ice pail experiment.

The result confirms the validity of Gauss's law and therefore of Coulomb's law.

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Van de Graaff electrostatic generator

Electric shielding

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Field at the surface of a conductor

35

0

E

Example The earth (a conductor) has a net electric charge. The resulting electric field

near the surface can be measured with sensitive electronic instruments; its average value

is about 150 V/m directed toward the center of the earth. (a) What is the corresponding

surface charge density? (b) What is the total surface charge of the earth?

Given the radius of the earth: R = 6.38106 m.

(a) = 0 E= -1.33 nC/m2

(b) Q = 4R2= - 680 kC = 4.21024 (-e)

This is compensated by an equal deficiency of electrons in the

earth's upper atmosphere, so the combination of the earth and

its atmosphere is electrically neutral.

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Problems

Young p. 742 Electric charge and electric field

21.2; 21.17; 21.28; 21.30; 21.33; 21.42; 21.53; 21.55; 21.61; 21.66; 21.67; 21.69;

21.73; 21.74; 21.88; 21.90; 21.93; 21.104;

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Young p. 773 Gauss's law

22.4; 22.9; 22.11; 22.12; 22.14; 22.17; 22.21; 22.23; 22.25; 22.30; 22.37; 22.38; 22.42;

22.45; 22.52; 22.56; 22.57; 22.58; 22.61; 22.63; 22.66;

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