Worksheet T: Electric potential.
 1 
1.
A metallic sphere of radius
a
is at the center
of a metallic shell of radii
b
and
c
. The net
charge of the sphere is
q
(
q
> 0). The net charge
of the shell is
−
3
q
.
Using Gauss’s law, one can
prove that:
E
= 0
(
r
<
a
)
E
=
kq/r
2
pointing out
(
a
<
r
<
b
)
E
= 0
(
b
<
r
<
c
)
E
= 2
kq/r
2
pointing in
(
r
>
c
)
a.
Some qualitative aspects, first: for points A to F, compare the value of the
electric potential for different pairs of points (choose one option for each pair):
To answer this, we need to look at the direction of the electric field: the electric
potential decreases in the direction of the electric field.
•
V
A
<
V
B
V
A
=
V
B
V
A
>
V
B
•
V
B
<
V
C
V
B
=
V
C
V
B
>
V
C
•
V
C
<
V
D
V
C
=
V
D
V
C
>
V
D
•
V
B
<
V
F
V
B
=
V
F
V
B
>
V
F
Notice that we did not need to fix the zero of the potential!
b.
And now the actual calculation. Let us choose the potential to be zero at infinity.
Find the potential for different points. Remember:
1
2
1
2
( )
(
)
r
r
V r
V r
E dl
−
= −
⋅
∫
G
G
•
For point A.
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 Fall '08
 HerreraSiklody
 Charge, Electric Potential, Energy, Potential Energy, Work, Electric charge, 0.030 M, Fnet Fnet=0 Fnet

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