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1
The Electric Potential
Alessandro Volta
(17451827)
This lecture: HRW 24.124.8
For next time: HRW 24.924.12
2
Last Time
•
E=0 in a conductor, and E is
⊥
to conducting
surfaces
•
Gauss’ Law can be used to determine E when E is
constant and perpendicular to a Gaussian surface
(imaginary).
Today
•
The
Electric Potential
•
Equipotential
surfaces
•
The electric potential of point charges
3
Potential Energy (review)
Potential energy
,
U
(r
)
,
describes a
conservative force.
The
reference point
, where U=0, is chosen for convenience.
For conservative forces, K+U=E, a constant.
kinetic
energy
total
energy
x
U
•Work
±
is
±path±
independent
.
• In a round trip, U is unchanged (conserved).
i
f
r
r
dW =F•ds
i
f
∆
U=U U=W
Change in
potential energy
Work
by the
field
Δ
∫
r
r
f
x
i
dU
F=
;
U=F•ds
dx
1
2
4
Electric Potential Energy
Interactive Lecture Question #7.1
What is the change in
potential energy
of a 3 C charge in a
uniform electric field of 10 N/C when it is moved along the
path shown?
5 m
initial
final
=−
∫∫
r
r
∆
U= dW= F•ds
Eq
∆
x
The potential energy gets lower (the charge would move to
the right on its own).
x
y
x
U
The reference
point for U is
arbitrary here
N
=10
3C 5m =150N m =150 J
C
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5
Electric Potential
Units:
Electric potential is measured in Volts (V).
1 J of work moves a 1 C charge across a 1 V potential
difference.
1 V = 1 J/C
The
electric potential
,
V(
r
)
, is typically used instead of the
electric potential
energy
, U(
r
).
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 Spring '07
 HUANG,TAIYIN
 Electric Potential, Gauss' Law, Magnetism

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