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Chapter 22 Electric charge
22-1 Electromagnetism
The early Greek philosophers knew that if you rubbed a piece of amber, it would attract bits of
straw. The Greeks also recorded the observation that some naturally occurring “stones” would attract
iron.
The sciences of electricity and magnetism developed separately for centuries – until 1820 when
Oersted found an electric current in a wire can deflect a magnetic compass needle.
The new science of electromagnetism (the combination of electrical and magnetic phenomena) was
developed further by research workers in many countries – Michael Faraday and later James Clerk
Maxwell.
22-2 Electric charge
An intrinsic characteristic of the fundamental particles making up those objects.
Two kinds: positive and negative
Electrical isolation: for example, a charged rod is suspended from a thread so that its charge cannot
change.
Charges with the same electrical sign repel each other, and charges with opposite electrical signs
attract each other.
22-3
Conductors: some of the negative charge can move rather freely.
Insulators (nonconductors): none of the charge can move freely.
Ground: setting up a pathway of conductors between an object and Earth’s surface.
Discharge: neutralizing the object by eliminating an unbalanced positive or negative charge.
Electrons: negatively charged
Protons: positively charged
Neutrons: electrically neutral
In atoms, for example copper, some of their outermost electrons do not remain attached to the
individual atoms but become free to more within the solid. These mobile electrons are called conduction
electrons.
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Demonstration of the mobility of charge in a
conductor.
Induced charge: some of its positive and
negative charges have been separated.
Semiconductors are materials that are
intermediate between conductors and insulators.
Superconductors: no resistance to the
movement of charge.
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The Si unit of charge is the coulomb: one coulomb is the amount of charge that is transferred through the
cross section of a wire in 1 second when there is a current of 1 ampere in the wire.
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If excess charge is placed on a spherical shell that is made of conducting material, the
excess charge spreads uniformly over the (external) surface.
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Six fixed charged particles where a=2.0cm and Θ=30ο.All six particles have the same magnitude of
charge, q=3.0*10-6C. What is the net electrostatic force F, acting on q, due to the other charges?
vfd
a
2a
F12=F14=
q1 q 2
1
4 0 ( 2a ) 2
F13=F15= F16=
1
q1 q 3
4 0
a2
F1=F16 - 2F13 sin 
=
1
40
q1 q 6
a
2
-
q1=q3 and   30
F1 =0
2
q1 q3
4 0
a2
sin 
Θ
a
a
a
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Quarks, the constituent particles of protons and neutrons, have charges of ±e/3 or ±2e/3,
but they apparently cannot be detected individually. For this and for historical reasons,
We do not take their charges to be the elementary charge.
An electrically neutral penny, of mass m=3.11g, contains equal amounts of positive and negative charge.
(a) Assuming that the penny is made entirely of copper, what is the magnitude q of the total positive (or
negative) charge in the coin?
(b) Suppose that the positive charge and the negative charge in a penny could be concentrated into two
separate bundles, loom apart. What attractive force would act on each bundle?
Sol:
(a) Z=29
N=NAm/M
q=NZe = 137000C
(b) F=
q2
=1.69X1016(N)
2
40 r
1
large!!
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Exercises:9,20,29,39
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Chater23
Question: If we move q1 toward q2, does the electric field q2, and thus the force acting onq2, change
immediately?
Answer: No. Electromagnetic wave at the speed of light C.
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The electric field exists independently of the test charge. (We assume that in our defining procedure, the
presence of the test charge does not affect the charge distribution on the charged object.)
Lines of force: electric field lines. A good way to visualize patterns in electric fields.
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Electric field lines extend away from positive charge and toward negative
charge.
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The nucleus of a uranium atom has a radius R of 6.8fm. Assuming that the positive charge of the nucleus
is distributed uniformly, determine the electric field at a point on the surface of the nucleus due to that
charge.
Sol: Z=92
E
1
Ze
=2.9X1021(N/C)
4 0 R 2
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Tactics: 1. the element ds, for instance
2. dq=λds

3. d E  ?
4. Symmetry
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A disk has a surface charge density σ of +5.3μC/m2 on its upper face. (This is a reasonable value for the
surface charge density on the photo sensitive cylinder of a photo copying machine, incidentally.)
(a) What is the electric field at the surface of the disk?
E

 3.0 X 10 5 N / C
2 0
(b) Using the binomial theorem, find an expression for the electric field at a point of the central axis far
from the disk.
(1  x) n  1 
Z
Z 2  R2
(1 
2

R 1 / 2
)
Z2
First order
n
n(n  1) 2
x
x  ...
1!
2!
Z
Z (1 
R2
)
Z2
 (1 
R 2 1 / 2
)
Z2
1
1 1
 (  1) 4
2
R
R
 1 2 2  2 2
 ....
1! Z
2!
Z4

R2
1
2Z 2
180
E

R2
1 q
[1  (1  1 
)] 
2
2 0
40 Z 2
2Z
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183
184
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Exercises: 19,30,33,51
186
Chapter 24
A new formation of coulomb’s law – Gauss’ law
Gaussian surface: a hypothetical closed surface central to Gauss’ law
Description: Gauss’ law relates the electric fields at points on a closed Gaussian surface
and the net charge enclosed by that surface.
Φ: The volume flow rate, volume per unit time.
υ: Uniform velocity
A: square loop of area
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First thought: repulsion reasonable.

Inside the conductor, E must be zero. If this were not so, the field would exert forces on
the conduction electrons, causing an electric current.
Important theorem: E=0 inside a conductor.
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(External electric field for conducting surface)
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202
Cf. Gravitation
Results: E 
{
r-2
r
r R
, r R
,
uniformly distributed
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Exercises:27,35,52,53
204
Chapter 25
Electrostatic force is a conservative force we can assign an electric potential energy U
to the system.
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Equipotential surfaces: a surface that all adjacent points have the same electric potential.
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210
(a) What is the electric potential V at a distance r=2.12x10 -10m from the nucleus of a
hydrogen atom?
(b) What is the electric potential energy U in electron-volts of an electron at the given
distance from the nucleus?
(c) If the electron moves closer to the proton, does the electric potential energy increase
or decrease?
Sol:
(a) V 
e (8.99 X 10 9 )(1.60 x10 19 )

 6.78V
40 r
2.12 X 10 10
1
(b)U=qv=(-1.60X10-19)(6.78)=-6.78eV
n
(c) Decreases V=
 Vi 
i 1
e n qi
 (n point charge)
40 r i 1 ri
1
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The potential at the center of a uniformly charged circular disk of radius R=3.5cm is V0=550V
(a) What is the total charge q on the disk?
(b) What is the potential at a point on the axis of the disk a distance Z=5.0R from the center of the disk?
Sol:
(a)Z=0,
V0=
2 V
R
  0 0
2 0
R
q=  (R 2 )  20 RV 0  1.1nC
(b)Z=5.0RV=

( (5.0r ) 2  R 2  5.0 R)  54V
2 0
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Exercises:24,41,53