Electric Potential Energy
and
Electric Potential
Chapter 24
Preview of Today’s Class
• Electric Potential Energy Difference
• Electric Potential Energy
• Electric Potential Difference
• Electric Potential
• Equipotential Surfaces
Electric Potential Energy Difference
Energy, ∆UE, to move a set of charges from initial to
final state is the electric potential energy difference
∆ U E = force × distance = ∫ F • d x
Charge moving in uniform electric field
∆ U E = E q x cos θ
Units :
N
•C•m → N•m → J
C
∆UE is work W done by ‘external agent’ (W=-Wsys)
q1
q1
q2
q2
x
Simple
example
Electric Potential Energy
Energy, UE, is the electric potential energy of the
configuration. It is same as electric potential energy
difference but assumes the ‘move’ is for charges that are
infinitely far apart to start with.
∞
U = UE = Uf – Ui =Uf, since Ui taken as zero
∞
q1
q2
q3
∞
Electric Potential Energy of Charge Configuration
Energy to assemble a group of charges
U = U12 + U 23 + U13
q1
q2
q3
kq1q2 kq2 q3 kq1q3
=
+
+
r12
r23
r13
What about positive and negatives?
Electric Potential Difference
(Property of the Field)
Change in energy/charge, ∆V, to move distance d in
electric field, E, is electric potential difference.
∆V =
∆U E
q
= work per charge
∆V = (force/charge) × distance = ∫Edx
Units: N/C × m → N·m/C → J/C → volt
+
σd
∆V =
ε0
∆V = ?
+
+
+
+
+
-
Electric Potential and Potential Difference
With Point Charges
Energy/charge, V, to move from infinity to a
position in electric field, E.
For a point charge:
 1
kq
kq
kq
1
and ∆ V =
V =
−
= kq 
− 
r
r2
r1
r1 
 r2
+
Sample Problems
17. (a) How far from a charge of +1.0 µC is a point
with an electric potential value of 10 kV?
(b) If the point were moved three times that
distance, how much of a potential change
would occur? Does it increase or decrease?
20. How much work is required to separate two
charges (each -1.4 µC) completely if they are
initially 8.0 mm apart?