Electric Potential
The quantity of electric potential is a very useful quantity in analyzing a wide variety of
problems in electricity. As we will see it will provides us with a simpler method of
calculating electric potential energy and electric fields.
To obtain an equation for the electric potential let’s begin by finding the work done by
the electric force on a positive charge as it moves in a uniform E-field.
+
+Q
+ + + + + + + + + + + + + + + + + ++
B
dl
+qo
E
d
FE
A
--------------------------
Q
B
w AB
B
FE d
FE
A
d
FE
FE qo d
A
wAB
qo Ed
Since the electric force is conservative, then
wAB
U AB
U AB
qo Ed
a) If qo > 0, then ΔUAB > 0 and WAB < 0.
b) If qo < 0, then ΔUAB < 0 and WAB > 0.
In general, U increases if a charge moves in opposite direction of electric force and
decreases if it moves in same direction.
Note that ΔUAB is the same value regardless of the path taken between A and B.
However, ΔUAB is proportional to the charge qo. If you double qo, then you also double
ΔUAB.
qo
q
2q
10q
ΔUAB
qEd
2qEd
10qEd
ΔUAB/ qo
Ed
Ed
Ed
1
Thus, the quantity ΔUAB/ qo is a constant value that is independent of the charge qo. We
define the quantity ΔUAB/ qo as the Electric Potential Difference.
VAB
VB VA
VA
VB
U AB
Electric Potential Difference
qo
UB
qo
UA
qo
UA
(Electric Potential at point A)
qo
UB
(Electric Potential at point B)
qo
V
U
Electric Potential
q
U
qV Electric Potential Energy
Therefore, if you know the electric potential at some point in space, then you can always
compute the electric potential energy of a charge q placed at that point.
Going back to our definition of Electric Potential Difference,
B
VAB
U AB
qo
WAB
qo
B
FE d
A
qo E d
A
qo
qo
B
V AB
VB V A
E d
Definition of Potential Difference
A
1.
2.
3.
4.
The SI unit of potential is the volt (V): 1 V = 1 J/C
Potential is a scalar quantity.
Only changes in potential have a physical meaning.
ΔV is a property of the E-field and independent of the charges placed in the Efield.
Wext AB
5. VAB
= work done per unit charge by an external agent in moving a
qo
charge qo from A to B against the electric force w/o changing its kinetic energy.
2
Potential Difference in a Uniform E-field
+
+Q
+ + + + + + + + + + + + + + + + + ++
B
dl
+qo
E
d
FE
A
--------------------------
Q
B
VAB
VB VA
B
E d
E
A
d
E
Ed
A
Or also,
VAB
VB VA
U AB
qo
qo Ed
qo
Ed
Point B is at a higher potential
E-field always points in the direction in which V decreases.
Positive charges move from a high potential to a low potential.
Negative charges move from a low potential to a high potential.
U AB
5. Since VAB
, potential difference is a measure of how much PE a charge
qo
can gain/lose.
1.
2.
3.
4.
3