d
−
d
≤
x
≤
d
(d)
ρ
x
( )
=
ρ
0
1
+
x
/
d
(
)
−
d
≤
x
≤
0
ρ
0
1
−
x
/
d
(
)
0
≤
x
≤
d
#
$
%
&
%
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12) An infinitely long cylinder of
radius R with uniform volume charge
density
ρ
0
has an offaxis hole of
radius b with center a distance d
away from the center of the cylinder.
What is the electric field within the
hole? Hint: Replace the hole by the
superposition of volume charge
distributions of density
ρ
0
and 
ρ
0
.
Convert the cylindrical coordinates to
Cartesian coordinates for ease of
vector additions.
13) Find the potential difference between the following surface charge distributions:
(a) Two parallel sheets of surface charge of opposite polarity ±
σ
0
and spacing a.
(b) Two coaxial cylinders of surface charge having infinite length and respective radii
a
and
b
.
The total charge per unit length on the inner cylinder is
λ
0
while the outer cylinder is 
λ
0
.
(c) Two concentric spheres of surface charge with respective radii R
1
and R
2
.
The inner
sphere carries a uniformly distribution surface charge with total charge q
0
.
The outer sphere
has total charge q
0
.
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 Summer '13
 BenjaminYellen
 Charge, Electric charge, Fundamental physics concepts, charge density

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