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Chapter 23
Electric Fields (cont.)
Dr. Jie Zou
PHY 1361
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Outline
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Electric field lines (23.6)
Motion of charged particles in a uniform
electric field (23.7)
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Practical application: The cathode ray tube
(CRT)
Dr. Jie Zou
PHY 1361
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Electric filed lines
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Pitfall prevention: Electric field lines are not
real.
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Electric field lines are related to the electric
field in the following manner:
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Dr. Jie Zou
Electric field lines are not material objects. They
are used only as a pictorial representation to
provide a qualitative description of the electric field.
The electric field vector E is tangent to the electric
field line at each point. The line has a direction,
indicated by an arrowhead, that is the same as that
of the electric field vector.
The number of lines per unit area through a
surface  to the lines is proportional to the
magnitude of the electric field in that region. Thus,
the field lines are close together where the electric
field is strong and far apart where the field is weak.
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Rules for drawing electric field
lines
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(1) The lines must begin on a positive charge
and terminate on a negative charge. In the
case of an excess of one type of charge,
some lines will begin or end infinitely far
away.
(2) The number of lines drawn leaving a
positive charge or approaching a negative
charge is proportional to the magnitude of
the charge.
(3) No two field lines can cross.
Dr. Jie Zou
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Electric field lines (I): for point
charges
Dr. Jie Zou
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Electric field lines (II): for two point
charges of equal magnitude
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Dr. Jie Zou
PHY 1361
Quick Quiz 23.5:
Rank the
magnitude of the
electric field at
points A, B, and
C.
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Electric field lines (III): for two point
charges of non-equal magnitude
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Quick Quiz: Which of the following
statements about the electric field
lines associated with electric
charges is false?
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Dr. Jie Zou
(a) Electric field lines can be either
straight or curved.
(b) Electric field lines can form closed
loops.
(c) Electric field lines begin on positive
charges and end on negative charges.
(d) Electric field lines can never
intersect with one another.
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Motion of charged particles in
a uniform electric field
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A uniform electric field E: constant in
magnitude and direction.
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Electric force: Fe = qE = ma (Newton’s
second law)
So, a = qE/m.
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Dr. Jie Zou
Example: The electric filed in the region
between two oppositely charged flat metallic
plates is approximately uniform.
If q is “+”, its a is in the same direction of the
electric filed E.
If q is “-”, it’s a is in the direction opposite the
electric filed E.
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Example 23.11 An accelerated
electron
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An electron enters the region of a
uniform electric field, with vi = 3.00
x 106 m/s and E = 200 N/C. The
horizontal length of the plates is l =
0.100 m.
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Dr. Jie Zou
(A) Find the acceleration of the electron
while it is in the electric field. Express a
in terms of unit vectors.
(B) If the electron enters the field at
time t = 0, find the time at which its
leaves the field. (Answer: 3.33 x 10-8 s)
(C) If the vertical position of the electron
as it enters the field is yi =0, what is its
vertical position when t leaves the field?
(Answer: -1.95 cm)
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What if? Problem #49, P. 737
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vi = 9.55 x 103 m/s.
Find
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Dr. Jie Zou
(a)  = ?
(b) Total time of flight t
=?
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Practical application: the
cathode ray tube (CRT)
Dr. Jie Zou
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Homework
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Ch. 23, P. 737, Problems: #40, 49.
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Chapter 24
Gauss’s Law
Dr. Jie Zou
PHY 1361
German mathematician and
astronomer (1777-1855) 13
Outline
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Electric flux (24.1)
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Electric flux through a surface
Electric flux through a closed surface
Dr. Jie Zou
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Electric flux
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(A) Suppose that the electric field is
uniform and the surface under
consideration is perpendicular to the
field, then E = EA.
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Dr. Jie Zou
E: electric flux through a surface area
A. SI unit: N·m2/C.
Electric flux is proportional to the
number of electric field lines penetrating
some surface.
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Electric flux (cont.)
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(B) Suppose the electric
field is uniform but the
surface is not
perpendicular to the field,
then E = EA cos .
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Dr. Jie Zou
PHY 1361
: the angle between the
electric field vector E and the
normal to the surface.
E is maximum = EA, when 
= 0°or when the surface is 
the field.
E = 0, when  = 90° or
when the surface is // to the
field.
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Electric flux (cont.): general
definition
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(C) In general, the electric field may
vary over a surface, and the surface is
not perpendicular to the field, the total
flux through the surface can be found
by:
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(1) Divide the surface into a large number
of small elements.
(2) Find the electric flux through each small
surface element: E = EiAi cos i = Ei·Ai
(scalar or dot product).
(3) Total electric flux (given by a surface
integral)
 E  lim
Ai 0
Dr. Jie Zou
 E  A
PHY 1361
i
i

 E  dA
surface
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Electric flux through a closed
surface
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At surface element 1: the field lines
leave the closed surface,  < 90° and
the electric flux > 0.
At surface element 2: the field lines
graze the surface,  = 90° and the
electric flux = 0.
At surface element 3: the field lines
enter the closed surface, 90° <  <
180° and the electric flux < 0.
The net electric flux through the
closed surface,  E   E  dA  En dA
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Dr. Jie Zou
The net flux through the surface is
proportional to the net number of lines
leaving the surface.
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Example 24.2 Flux through a
cube
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Consider a uniform
electric field E oriented in
the x direction. Find the
net electric flux through
the surface of a cube of
edge length l, oriented as
shown in the figure.
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Dr. Jie Zou
Answer: 0.
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Homework
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Ch. 24, P. 761, Problems: #5.
Dr. Jie Zou
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