Electric Potential

1. Course of lectures
«Physics»
Lecture №9

2. Potential Difference and Electric Potential.
Potential Differences in a Uniform
Electric Field. Electric Potential and Potential
Energy Due to Point Charges.

3. The Electric Field
An electric field is said to exist in the region of space around a
charged object—the source charge. When another charged object—
the test charge—enters this electric field, an electric force acts on it.
The electric field vector E
at a point in space is
defined as the electric force
Fe acting on a positive test
charge q0 placed at that
point divided by the test
charge:

8. The Gravitational Analogy Revisited

9. The Gravitational Analogy Revisited

10. Electric Potential
The electric field intensity is
acting as a force on any charges
it arrives upon.
Therefore in moving a unit
charge from P1 to P2, work must
be done against the field.
 0
F q E

11. Electric Fields and WORK
In order to bring two like charges near each other work
must be done. In order to separate two opposite
charges, work must be done. Remember that whenever
work gets done, energy changes form.
As the monkey does work on the positive charge, he increases the energy of
that charge. The closer he brings it, the more electrical potential energy it
has. When he releases the charge, work gets done on the charge which
changes its energy from electrical potential energy to kinetic energy. Every
time he brings the charge back, he does work on the charge. If he brought
the charge closer to the other object, it would have more electrical potential
energy. If he brought 2 or 3 charges instead of one, then he would have had
to do more work so he would have created more electrical potential
energy. Electrical potential energy could be measured in Joules just like any
other form of energy.

13. Electric Fields and WORK
Consider a negative charge
moving in between 2
oppositely charged parallel
plates initial KE=0 Final KE=
0, therefore in this case Work
= DPE
We call this ELECTRICAL potential
energy, UE, and it is equal to the
amount of work done by the
ELECTRIC FORCE, caused by the
ELECTRIC FIELD over distance, d,
which in this case is the plate
separation distance.
Is there a symbolic relationship with the FORMULA for gravitational
potential energy?

14. Electric Potential
Ed
q
W
qEd
W
U
d
x
h
E
g
q
m
W
or
U
U
mgh
U
E
E
g
g








)
(
)
(
Here we see the equation for gravitational
potential energy.
Instead of gravitational potential energy we are
talking about ELECTRIC POTENTIAL ENERGY
A charge will be in the field instead of a mass
The field will be an ELECTRIC FIELD instead of
a gravitational field
The displacement is the same in any reference
frame and use various symbols
Putting it all together!
Question: What does the LEFT side of the equation
mean in words?
The amount of Energy per charge!

16. Energy per charge
The amount of energy per charge
has a specific name and it is
called, VOLTAGE or ELECTRIC
POTENTIAL (difference). Why
the “difference”?
q
mv
q
K
q
W
V
2
2
1

D


D

17. Understanding “Difference”
The charge travels through
a “change in voltage”
much like a falling mass
experiences a “change in
height.
(Note: The electron does
the opposite)

19. BEWARE!!!!!!
W is Electric Potential Energy
(Joules)
is not
V is Electric Potential
(Joules/Coulomb)
a.k.a Voltage, Potential
Difference

21. The “other side” of that
equation?
Ed
q
W
qEd
W
U
d
x
h
E
g
q
m
W
or
U
U
mgh
U
E
E
g
g








)
(
)
(
Since the amount of energy per charge is called
Electric Potential, or Voltage, the product of the
electric field and displacement is also VOLTAGE
This makes sense as it is applied usually to a set
of PARALLEL PLATES.
DV=Ed
E
d
DV

22. Potential Difference
• Electric Potential Difference is a change in
electric potential – a change in the ability
to do work:
∆V = PEelectric
q
SI unit is the Volt = Joule/Coulomb
As a 1 coulomb charge moves through a
potential difference of 1 volt, the charge
loses (or gains) 1 joule of energy

23. When force is applied to move an object,
work is the product of the force and the
distance the object travels in the direction of
the force














2
1
2
1
2
1
2
1
0
field
e
against th
charge
the
moves
force
the
since
but
P
P
P
P
P
P
P
P
l
d
E
q
W
S
d
E
Q
S
d
E
Q
S
d
F
W
   
int 0
W F dS q E dS
    
int 0
dU W q E dS

24. Therefore without specifying the path
 


2
1
P
P
l
d
E
Q
W
E
P1
P2
The scalar line integral of an
Irrotational (conservative) E
field is path-independent
 
 0
l
d
E
0
q
U
V 
S
d
E
q
U
V
P
P



D

D 
2
1
0
1
2 P
P V
V
V 

D

25. Equipotential surfaces
Consider the plot of the
electrostatic potential contours
forming equipotential surfaces
around the point charge
superimposed over the field
lines for the point charge
A set of points with same potential forms equipotential
surface. For a point charge, equipotentials are spheres
at fixed radius r.

28. As we can notice the field goes into the direction of
decreasing potential
If the behavior of the potential is unknown, the electric
intensity field can be determined by finding the maximum
rate and direction of the spatial change of the potential
field
V
E 


29. By using the above in the following equation
we get
 


2
1
P
P
l
d
E
Q
W


















2
1
2
1
2
1
2
1
1
2
)
(
P
P
P
P
l
P
P
P
P
V
V
dV
dl
a
V
l
d
V
l
d
E
Potential difference

30. 






















 

Q
W
V
R
Q
V
V
V
R
R
Q
R
Q
a
dR
a
R
Q
l
d
E
V
P
P
P
P
R
R
P
P
P
P
0
1
2
0
0
2
0
21
4
1
1
4
4
4
2
1
2
1
2
1
2
1




Absolute potential at some finite
radius from a point charge fixed at
the origin (reference voltage of zero
at an infinite radius)
Work per Coulomb required to pull a
charge from infinity to the radius R

31. For a collection of charges of continuous
distribution
(V)
4
1
(V)
4
1
4
(V)
4
1
0
0
0
0
dl
R
V
ds
R
V
R
dQ
V
dv
R
V
l
l
s
s
v
v















