Physics 4322
Homework Set 2
January 24, 2012
Due: Tuesday, January 31, 2012
1. A wire has resistance
R
.
Determine the resistance of a wire twice the length and half the
diameter, assuming it is made from the same material.
2. A conducting sphere of radius
a
is embedded in a large volume filled with a material with
conductivity
.
The sphere is held a constant potential
V
o
with respect to the boundary, which
may be assumed to be at infinity.
Determine the current density
J
(
r
), the total current
I
, and the
resistance
R
.
(Hint: Laplace’s equation for
V
must be satisfied.)
3. Two concentric conducting spherical shells having inner and outer radii
a
and
b
, respectively,
are separated by a weakly conducting material of conductivity
.
(a) If the potential difference
between the spheres is
V
, what current
I
exists between the spheres? (b) What is the resistance
R
between the shells?
4. Suppose the conductivity of a material between two concentric cylinders is
given by
(
s
) =
k
/
s
.
Calculate the resistance
R
between the cylinders.
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 Resistance, Work, Magnetic Field, loop

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