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Name____
SOLUTIONS
_______
Physics 125: Analytical Physics II
Quiz 2/20/08
The picture shows the crosssection of a thick spherical
shell, with outer radius
12.0cm
b
=
and inner radius
6.0cm
a
=
.
The insulating material of the shell carries
a uniform charge density of
3
32.0μC / m
ρ
=
.
Use Gauss’ Law to determine a formula for the electric
field strength at a distance
r
from the center, where
arb
<<
.
Your answer should be a function of
r
, but
all parameters in the function should be numerically
evaluated.
Choose a Gaussian surface: a sphere of radius
r
(has the
same symmetry as the charge, and passes through the point
where we want to know the field).
Apply Gauss’ Law:
0e
n
c
E
q
ε
Φ=
Lefthand side:
By symmetry, everywhere on the Gaussian surface, the Efield has constant
magnitude and is perpendicular to the surface (parallel to
dA
G
).
Thus, as always for spherical
symmetry,
2
4
Er
r
AE
r E
π
=
Righthand side:
The volume of the object (vertical lines in this picture) that is
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 Spring '08
 IYER
 Physics, Charge

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