PHY127 Summer Session I I

PHY127 Summer Session II• Most of information is available at: http://nngroup.physics.sunysb.edu/~chiaki/PHY127-08

• 5 homework problems for each chapter are in general due a week later at 11:59 pm and are delivered through MasteringPhysics website at: http://www.masteringphysics.com. You need to open an account.

• In addition to homework problems, there is naturally a reading requirement of each chapter, which is very important.

• The website above is the point of contact outside the class for important messages, so regularly and frequently check the website.• At the end of class a quiz is given for the previous chapter covered in the class. Bring a calculator (no wireless connection), a pencil, an eraser, and a copy of lecture note for the chapter.• The lab session is an integrated part of the course and make sure that you will attend all the sessions. See the syllabus for the detailed information and the information (e.g. lab manuals) at the website above.

Chapter 20: Electric Charge/Force/Field

Electric charge

Two opposite signed charges attract each other

Two equally signed charges repel each other

When a plastic rod is rubbed with a piece of fur, the rod is “negatively” charged

When a glass rod is rubbed with a piece of silk, the rod is “positively” charged

Electric charge is conserved

Electric charge (cont’d)

Particle Physics

Model of Atoms

electrons e-

nucleus

Old view

Semi-modern view

Modern view

nucleusquarks

What is the world made of?

• Electron: Considered a point object with radius less than 10-18 meters with electric charge e= -1.6 x 10 -19 Coulombs (SI units) and mass me= 9.11 x 10 -

• Proton: It has a finite size with charge +e, mass mp= 1.67 x 10-27 kg and with radius– 0.805 +/-0.011 x 10-15 m scattering experiment– 0.890 +/-0.014 x 10-15 m Lamb shift experiment

• Neutron: Similar size as proton, but with total charge = 0 and mass mn=– Positive and negative charges exists inside the neutron

• Pions: Smaller than proton. Three types: + e, - e, 0 charge.– 0.66 +/- 0.01 x 10-15 m

• Quarks: Point objects. Confined to the proton and neutron,– Not free– Proton (uud) charge = 2/3e + 2/3e -1/3e = +e– Neutron (udd) charge = 2/3e -1/3e -1/3e = 0– An isolated quark has never been found

• Two kinds of charges: Positive and Negative• Like charges repel - unlike charges attract• Charge is conserved and quantized

1. Electric charge is always a multiple of the fundamental unit of charge, denoted by e.

2. In 1909 Robert Millikan was the first to measure e.Its value is e = 1.602 x 10−19 C (coulombs).

3. Symbols Q or q are standard for charge.4. Always Q = Ne where N is an integer5. Charges: proton, + e ; electron, − e ; neutron, 0 ; omega, − 3e ;

quarks, ± 1/3 e or ± 2/3 e – how come? – quarks always exist in groups with the N×e rule applying to the group as a whole.

Charging by contact

Charging by induction (cont’d)

Conductors, insulators, and induced charges

Conductors : material in which charges can freely move. metal Insulators : material in which charges are not readily transported. wood Semiconductors : material whose electric property is in between. silicon Induction : A process in which a donor material gives opposite signed charges to another material without losing any of donor’s charges

Coulomb’s law

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

kF r : distance between two chargesq1,q2 : chargesk : a proportionality constant

- The directions of the forces the two charges exert on each other are always along the line joining them.- When two charges have the same sign, the forces are repulsive.- When two charges have opposite signs, the forces are attractive.

F2 on 1 F1 on 2 F2 on 1 F1 on 2 F1 on 2F2 on 1

Coulomb’s law

Coulomb’s law and units

kF r : distance between two charges (m)q1,q2 : charges (C)k : a proportionality constant (=ke)

C/mN100.9

C/mN10988.8

C/mN10987551787.8

s/m102.99792458c 8

)mN/(C10854.8;4

1c)C/sN10(

SI units

Exact by definition

C10)63(602176462.1 19echarge of a proton

C10nC1 -9

Coulomb’s law

Example: Electric forces vs. gravitational forces

electric force

gravitational force

)kg1064.6(C)102.3(

kg/mN1067.6C/mN100.9

Gravitational force is tiny compared with electric force!

kg1064.6

102.3227

0protonneutron

particle

Coulomb’s law

Example: Forces between two charges

9-9229

N 019.0m)030.0(

C)10C)(751025()C/mN100.9(

nC75nC,25 21 qq

F1 on 2F2 on 1

cm0.3r

1on22on1 FF

Coulomb’s law

Superposition of forces Principle of superposition of kforces

When two charges exert forces simultaneously on a third charge,the total force acting on that charge is the vector sum of the forcesthat the two charges would exert individually.

Example: Vector addition of electric forces on a line

+ -2.0 cm

F1 on 3F2 on 3

q1q2q3

4.0 cm

Coulomb’s law

Example: Vector addition of electric forces in a plane

N29.0m)50.0(

C)10C)(2.0100.4()C/mN100.9(

6-6229

QQon r

0.50 m

0.40 m0.30 m

0.30 m

q1=2.0 C

q2=2.0 C

Q=4.0 C

xQonF )( 1

yQonF )( 1

N23.00.50m0.40mN)29.0(cos)()( 11 QonxQon FF

N17.00.50m0.30mN)29.0(sin)()( 11 QonyQon FF

0N17.0N17.0N0.460.23NN23.0

force due to q2

Electric field and electric forces

remove body B

•Existence of a charged body A modifies property of space and produces an “electric field”. •When a charged body B is removed, although the force exerted on the body B disappeared, the electric field by the body A remains. •The electric force on a charged body is exerted by the electric field created by other charged bodies.

Electric field and electric forces (cont’d)

A Test charge

placing a test charge

• To find out experimentally whether there is an electric field at a particular point, we place a small charged body (test charge) at point.• Electric field is defined by

(N/C in SI units)

• The force on a charge q: EqF

Electric field of a point charge

rrr /ˆ

r̂ r̂P P

rrqE ˆ

'' EErr

Electric field and electric forces Electric field by a continuous charge distribution

Electric field and electric forces Electric field by a continuous charge distribution (cont’d)

These may be considered in 1, 2 or 3 dimensions.

There are some usual conventions for the notation:

Charge per unit length is λ ; units C/m i.e, dq = λ dl

Charge per unit area is σ ; units C/m2 i.e, dq = σ dA

Charge per unit volume is ρ ; units C/m3 i.e, dq = ρdV

Example : Electron in a uniform fieldy

1.0 cm -E

Two large parallel conducting plates connected to a battery produce uniform electric field N/C1000.1 4E Since the electric force is constant, the acceleration is constant too

m/s1076.1kg1011.9

N/C)10C)(1.001060.1(

From the constant-acceleration formula: )(2 020

2 yyayyy

0,0m/s109.52 00y6 yyayy when cm0.1y

The electron’s kinetic energy is: J106.1)2/1( 172 mK

The time required is: sa

yy 90 104.3

Electric field lines 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.

Electric field lines show the direction of at each point, and their spacing gives a general idea of the magnitude of at each point.

Where is strong, electric field lines are drawn bunched closely together; where is weaker, they are farther apart.

At any particular point, the electric field has a unique direction so that only one field line can pass through each point of the field. Field lines never intersect.

Electric field lines

• E-field lines begin on + charges and end on - charges. (or infinity)

• They enter or leave charge symmetrically.• The number of lines entering or leaving a

charge is proportional to the charge.• The density of lines indicates the strength

of E at that point.• At large distances from a system of charges,

the lines become isotropic and radial as froma single point charge equal to the net chargeof the system.

• No two field lines can cross.

Field line drawing rules: Field line examples

Electric field lines (cont’d) Field line examples (cont’d)

Electric Dipoles An electric dipole is a pair of point charges with equal magnitude and opposite sign separated by a distance d.

electric dipole moment

Water molecule and its electric dipole

Electric Dipoles Force and torque on an electric dipole

)sin)(( dqEqdp

torque:electric dipole moment:

work done by a torque during an infinitesimal displacement d

dpEddW sin

Electric Dipoles Force and torque on an electric dipole (cont’d)

coscos)sin(

pEpEdpEdW

cos)(potential energy for a dipolein an electric field

Exercises Trajectory of a charged particle in a uniform electric field

Exercises Cathode ray tube

Exercises Electric field by finite line charge

Exercises Electric field by a ring charge

Exercises Electric field by a uniformly charged disk

Exercises Electric field by infinite plate charge

+++++++

Exercises Electric field by two oppositely charged parallel planes

Exercises Far field by an electric dipole

d cos)2/(d

cos2dRR cos

1cos12

cos214

1when1)1( xnxx n

PHY127 Summer Session I I

Documents

I Phone Session Mufix

Session I Angelo Moreno

Session I moodle

Session i ppt

Chemistry. CHEMICAL BONDING – SESSION I Session Opener

E-Government Session I

Session I-Business Environment

NC Plan Session I

CSW Session I

Session I: Tuesday, January 18, 2022 Session II: Friday

Session 3 (i)

FBS Session I

Tata QnA session I

Session 4 i

PHY127 Summer Session II - Stony Brook Universitynngroup.physics.sunysb.edu/~chiaki/PHY127-08/Notes/Chap20.pdf · PHY127 Summer Session II ... Two opposite signed charges attract

Scm Session I

Teaching aids session-i

Chapter 23: Electrostatic Energy and Capacitancenngroup.physics.sunysb.edu/~chiaki/PHY127-08/Notes/Chap23.pdf · Chapter 23: Electrostatic Energy and Capacitance ... Energy Storage

Algebra I Extended Session

I pad session