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Lecture 81
Electric
Potential Energy
of a Charge (continued)
0
( )
( )
r
i
U
U r
U i
q E dl
i
is “the”
reference point
.
Choice of reference point
(or
point of zero potential
energy
) is arbitrary.
0
dl
i
is often chosen to be
infinitely far (
)
l
d
E
q
dW
0
l
d
E
q
dU
0
r
i
l
d
E
q
0
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View Full Document Lecture 82
Electric
Potential
•
So
U(
r
)/q
0
is independent of q
0
, allowing us to introduce
electric potential V
independent of q
0
.
0
()
Ur
Vr
q
•
[Electric potential] = [energy]/[charge]
SI units:
J/C = V
(volts)
•
U(
r
)
of a
test charge q
0
in electric field generated by
other source charges is
proportional to q
0
.
0
q
taking the same
reference point
Potential energy difference when
1 C
of charge is
moved between points of potential difference
1 V
1
J
Scalar!
Lecture 83
Two Ways to Calculate Potential
• Integrate

E
from the reference point (∞) to the point (
P
) of
observation:
P
V r
E dl
• Integrate
dV
(contribution to
V(r)
from each infinitesimal
source charge
dq
) over all source charges:
A
line integral
(which could be tricky to do)
If
E
is known and simple and a simple path can be used,
it may be reduced to a simple, ordinary 1D integral.
q
1
q
2
q
3
q
4
P
Q
P
r
P
Q
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View Full Document Lecture 84
Equipotential Surfaces
•
An
equipotential
surface is a surface on which the
potential is the same everywhere.
0
0
U
V
q
For a displacement Δr of a test
charge q
0
along an equipotentital
,
0
E
UW
U = constant on an equipotential surface.
E is
everywhere perpendictular to U
V
E
r
Potential difference between nearby equipotentials is
approximately equal to E times the separation distance.
Equipotential surfaces are drawn at constant intervals of ΔV
http://www.its.caltech.edu/~phys1/java/phys1/EField/EField.html
r
E
q
0


r
E
Lecture 85
Potential and Conductors
• Entire conductor including its
surface(s) has
uniform
V
.
Equipotential
surfaces
• Draw equipotential surfaces
outside the conductor on which
V
is
uniform.
0
E dl
For Δ
l
on equipotential, or
equipotential surface
0
V
E
l
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View Full Document Lecture 86
Electrostatic
Potential Energy
of Conductors
bring
dq
in from ∞
q+dq,
v
+d
v
v
kq
U
W
dq
dq
R
Spherical
conductor
q,
v
R
Total work to build charge
from 0 up to Q:
2
0
1
22
Q
kq
kQ
U
U
dq
QV
RR
q
v
dq
U
Q
V
kq
v
r
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