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Chapter 23 Electric Potential
• When a charged particle moves in an electric field, the
field exerts a force that can do work on the particle.
• Just as gravitational potential energy depends upon the
height of the mass above the earth’s surface, electric
potential energy depends upon on the position of the
charged particle in the electric field.
Chapter 23
1
Potential and Kinetic Energy
Work done by a Force on a particle that moves from point a
to point b.
Potential and Kinetic Energy
K=Kinetic Energy U= Potential Energy
Chapter 23
2
Electric Potential Energy (joules)
Electric Potential Energy in a Uniform Electric Field
b 

b
Wab   F  dl   F cos  dl
a
a
F  q0 E
Wab  Fd  q0 Ed
(Uniform electric field)
where Ua is the potential energy at point a and Ub is the potential energy at point b.
Chapter 23
3
Electric Potential Energy
Figure 23-3
Chapter 23
4
Electric Potential Energy
Figure 23-4
Chapter 23
5
Electric Potential Energy
Electric potential energy distance r away from a point charge
rb


rb
rb
ra
ra
Wa b   Fr  dr   Fr cos dr   Fr dr
ra
qq0
qq0  1 1 
   (23-8)
  Fr dr  
dr 
2
40 r
40  ra rb 
ra
ra
rb
Wab
Wab
rb
1
qq0  1  qq0  1 
  
   U a  U b

40  ra  40  rb 
joules
where Ua = potential energy at point a and Ub = potential energy at point b
As rb

Wa
qq0  1 
   U a = Potential energy of q0

40  ra 
between point a and
Figure 23-5
infinity.
where U is the potential energy of q0 at any distance r away from a point charge q.
Chapter 23
6
Electric Potential Energy is path independent
Figure 23-5
cos dl  dr
rb


rb
rb
ra
ra
Wa b   Fr  dl   Fr cos dl   Fr dr
ra
Chapter 23
7
Electric Potential Energy
Electric potential energy distance r away from many point charges
The total potential
energy is the algebraic
sum of the individual
charge energy
q0 q1
q0 q2
q0 q3
q0
Ua 



40 r1 40 r2 40 r3 40
Chapter 23
 q1 q2 q3 
 


r2
r3 
 r1
8
Electric Potential (Voltage) = Potential Energy per unit charge
Wab
a
b
Vab 
F
Definition
E
·
·
q0
+q
0
1 volt = 1 joule/coulomb = J/C
Vab 
Va 
Wab U a  U b U a U b



 Va  Vb
q0
q0
q0
q0
Ua
q0
Vb 
volts
b 

Ub
q0
Wab  q0Vab
volts
Note:
1 ev = (1.6 x 10-19) joules
b
Wab   F  dl   q0 E  dl
a
Vab
W
1
 ab 
q0
q0
a
b
q
joules
b
0
E  dl   E  dl
a
a
Chapter 23
9
Electric Potential (Voltage)
Electric potential distance r away from a point charge
qq0
Ua 
40 ra
1
Ua
1 q
Va 

q0 40 ra
Ub 
qq0
40 rb
1
Ub
1 q
Vb 

q0 40 rb
Vab  Va  Vb
Figure 23-5
Chapter 23
10
Electric Potential (Voltage)
Electric potential distance r away from many point charges
The total Electric
Potential is the algebraic
sum of the individual
potentials
Ua
q3
q1
q2
1  q1 q2 q3 
 
Va 




 
q0 40 r1 40 r2 40 r3 40  r1 r2 r3 
Chapter 23
11
Electric Potential (Voltage)
Example 23-4
q1 = q2 = 12 nC
Figure 23-13
Chapter 23
12
Electric Potential (Voltage)
Example 23-7
K a  U a  Kb  U b
0  U a  Kb  U b
Kb  U a  U b
1
2
K b  mvb  q0 (Va  Vb )  q0Vab
2
U a  q0Va
U b  q0Vb
U a  U b  q0Va  q0Vb  q0 (Va  Vb )
Chapter 23
vb 
2q0 (Va  Vb )
m
13
A Charged Conducting Sphere – Electric Field and Electric Potential
Inside the sphere E = 0
every where
Inside the sphere V is the
same every where
( assume a point charge q)
b
Vab 
Figure 23-17
Chapter 23
 E  dl
a
14
Ionization and Corona Discharge
For air to be ionized at the surface of the
sphere E > 3 x 106 V/m
What is V at the surface?
p.795
Chapter 23
15
Calculating Electric Potential
Example 23-9 Oppositely Charged Parallel Plates
Uniform Electric Field
b
b
a
a
Vab   E  dl   E cos dl Ed
From section 22.4
 coul/m2 charge

0
  0E
   0Vab / d
E
Vab = Ed
Figure 23-18
A way of
measuring charge
density
 coul/m2 charge
Chapter 23
16
Calculating Electric Potential
Example 23-10 Difference in Potential between two points outside
an Infinite Line Charge or Charged Conducting Cylinder.
b
a
1 
Er 
20 r

Vab   E  dl   E cos dl   Er dr 
20
a
a
r
b
b
rb
a
Vab
rb


ln
20
ra
Chapter 23
rb
dr
r r
a
17
Equipotential Surfaces (Chapter 23, Sec 4)
·
l
a
E
·
b
Equipotential surface (always perpendicular to E)
b
b
a
a
Vab   E  dl   E cos dl
  90
cos   0
Vab  Va  Vb  0
Va  Vb
Chapter 23
18
Equipotential Surfaces
Figure 23-23
Chapter 23
19
Equipotential Surfaces
Equipotential Surfaces and Conductors
Figure 23-25
E parallel = 0. Therefore, E is perpendicular to the surface.
This makes the surface of the conductor an equipotential surface.
Chapter 23
20
Potential Gradient (Chapter 23, Sec 5)
a
b
·
E
·
If cos  = 1 ( = 0o)
b
b
b
a
a
a
b
a
b
a
Vab   E  dl   E cos dl   Edl
Vab   dV    dV
b
b
a
a
  dV   Edl
 dV  Edl
E
dV
dl
potential gradient
Chapter 23
21
Chapter 23
22
Chapter 23
23