AP B CH 17: ELECTRIC POTENTIAL
ELECTRIC POTENTIAL
Recall Energy is a conserved quantity in
mechanics. This law is helpful for studying
charges as well.
 When a charge, q, moves from some point, b,
to another point, a, it’s energy changes by the
amount of work done on it with respect to the
electric field. (Work done by the field, PE
decreases; Work done on the field, PE
increases)

ELECTRIC POTENTIAL

Electric Potential, V, is defined as the
PEa
potential energy per charge. Va q It is
also sometimes called Potential Energy and
is measured in Voltage, (volts), V.
ELECTRIC POTENTIAL
The electric potential V is defined in terms of the work to be
done on a charge to move it against an electric field.
The electric potential V is a scalar quantity defined as the
potential energy per unit charge.
VA
PE A
q
Units: J/C = Volt (V)
As discussed in the energy chapter, only differences in potential
are measurable.
We find the potential difference between two points A and B to
be equal to:
VAB
VA VB
WBA
q
In other words the potential
difference between two points
is the work per unit positive
charge done by electric forces
in moving a small test charge
from the point of higher
potential to the point of lower
potential.
Since the electric potential is defined as the potential energy per
unit charge, then the change in potential energy of a charge q
when moved between two points A and B is:
ΔPE = PEB - PEA = qVBA
The potential at a point is defined in terms of a positive charge.
The potential due to a positive charge is positive, and the
potential due to a negative charge is negative.
The potential is the same at equal distances from a spherical
charge. The dashed lines in the figure below are called
equipotential lines. Note that the lines of equal potential are
always perpendicular to the electric field lines.
POTENTIAL AND ELECTRIC FIELD
The potential difference between two oppositely charged plates
is equal to the product of the field intensity and the plate
separation.
W = q VBA
W = F d = q Ed
(d is distance)
VBA = E d
Units: VBA = Volts (V)
E = V/m or N/C
4. The potential difference between two plates 5 mm apart is 10 kV.
Determine the electric field intensity between the two plates.
r = 5x10-3 m
V = 10x103 V
E
V
d
10 x103
6 V/m
=
2x10
5x10 3
ELECTRIC POTENTIAL due to POINT CHARGES
The potential V at a point a distance r from a charge Q is equal
to the work per unit charge done against electric forces in
bringing a positive charge +q from infinity to that point.
In other words, the potential at some point A as shown in the
figure, is equal to the potential energy per unit charge.
A
VA
Q
k
r
Units: J/C = Volt (V)
The potential in the vicinity of a number of charges is equal to
the algebraic sum of the potentials due to each charge.
V = V1 + V2 + V3 + ........... + VN
= (Qi/ri)
V
kQ
r
Units: Volts (V)
5. What is the electric potential at the center of a square of sides equal 1 m
if the charges placed at the corners are +1 nC, -2 nC, +3 nC and -4 nC
(read in a CW direction)
+1
-2
The center of the square is
equidistant from all four charges, a
d
distance r of
2
-4
+3
V = V1 + V2 + V3 + V4
V
kq1
r
kq2
r
kq3
r
kq4
r
k
9 x109 (1 2 3 4) x10 9
(q1 q2 q3 q4 )
= - 25 V
1
r
2
ELECTRIC POTENTIAL ENERGY
The electric potential energy of a system composed of a charge
q and another charge Q separated by a distance r is equal to
the work done against the electric forces in moving a charge +q
from infinity to that point.
PE
qQ
k
r
Joules (J)
Whenever a positive charge is moved against an electric field,
the potential energy increases; whenever a negative charge
is moved against an electric field, the potential energy
decreases.
6. A charge of + 2 nC is 20 cm away from another charge of
What is the potential energy of the system?
q = +2 nC
Q = + 4 μC
r = 20 cm
PE
kQq
r
+ 4 μC. a.
9 x109 (4 x10 6 )(2 x10 9 )
0.2
= 36x10-5 J
b. What is the change in potential energy if the 2 nC charge is moved to a
distance of 8 cm from the 4 μC charge?
r = 8 cm
PE
9 x109 (4 x10 6 )(2 x10 9 )
= 90x10-5 J
0.08
ΔPE = 90x10-5 - 36x10-5
= 54x10-5 J
YOUR TURN TO PRACTICE

Please do Ch 17 Review pg 522 #s 1-7,13,&14