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Lecture 10
Electric Potential Energy and
Electric Potential
Electric potential energy
Electric forces are conservative (Coulomb’s law is
mathematically identical to Newton’s gravitational force,
which is conservative).
So we can write the work done by them as a change in
potential energy.
B
A to B
B
A
A
W
Fdl
U
U U
Electric potential energy of two point charges
A test charge
q
moves from point A to point B near another charge
Q
.
The work done by the electric force is:
B
A to B
A
BA
ee
Qq
kk
rr
B
A
r
e
qQ
k
B
A
2
dr
B
A
B
A
( )
constant
Ur
Electric potential energy
function for two point charges
UU
Example: Electric potential energy.
Three charges
= 3.0 nC are initially fixed at the corners
of an equilateral triangle of side
a
= 1.0 cm. One of them is
released. Find its kinetic energy when it has doubled the
distance to each of the other two charges.
= 3.0 nC
= 1.0 cm
2
2
29
2
9
f
2
Nm
(3.0 10 C)
22
(
9
1
0
)
8
.
1
J
2
C
2(0.01 m)
Kk
ii ff
KUK U
f
02
2
2
kK
aa
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ACT: Stored energy
What is the electric energy stored in a system of three
charges
q
= 3.0 nC that form an equilateral triangle of side
a
= 1.0 cm? (with
U
infinity
= 0)
= How much energy did I put in the system when I built it?
= How much work was done to built it?
= 3.0 nC
= 1.0 cm
The stored energy is:
A. Positive.
B. Negative.
C. Zero.
We have to push the charges to arrange them like this
→
Add energy
Or: Unless charges are somehow fixed, they will move to a situation
with less energy (
infinity
= 0).
i
f
()
UUU
Work to bring the first charge
from infinity:
= 3.0 nC
= 1.0 cm
ext,2
i
f
WU
Work to bring the second charge
from infinity:
29
2
N(
3
0
1
0
C
)
2
0
k
ext,1
by E field,1
WW
000
22
ext,3
i
f
0
qq
kk
aa
Work to bring the third charge
from infinity:
total
stored
0 8.1 16.2
24.3 J
(> 0, as expected)
W
9
2
Nm
(3.
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This note was uploaded on 09/21/2011 for the course PHYS 222 taught by Professor Johnson during the Spring '07 term at Iowa State.
 Spring '07
 Johnson
 Physics, Electric Potential, Energy, Force, Potential Energy, Work

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