ECE 329
Homework 5
Due: Oct 5, 2010, 5PM
1.
Conductance
 Copper is a highly conducting material with a conductivity of
σ
= 5
.
8
×
10
7
S/m and
a freeelectron density of
N
e
= 8
.
45
×
10
28
m

3
.
a) Given that the charge of an electron is
q
=

e
=

1
.
6
×
10

19
C, calculate the DC electron
mobility for copper.
b) Determine the resistance R of a copper wire of radius
r
= 1
mm and length
l
= 1
km.
c) What would be the magnitude of the electric field

E

within the wire of part (b) if the wire
were conducting a current of
1
A? You may assume uniform current distribution across the cross
section of the wire.
d) How long would it take for an electron to drift from one end of the wire to the other?
2.
Capacitance of a charged sphere
 Consider a metallic, spherical shell or radius
a
= 1
m, with its
center coinciding with the origin of the reference coordinate system.
The medium exterior to the
sphere has permittivity
= 4
o
and conductivity
σ
= 10

6
S/m. This configuration  a conducting
shell inside an infinite medium of permittivity
 can be thought of as a spherical capacitor consisting
of two concentric spherical conductors, one with radius
r
=
a
and the other of infinite radius. The
figures below show how the configuration containing only a single conducting shell (rightmost figure)
is related to a spherical capacitor with two, nested conducting shells, both with finite radii. As you
can see the capacitance of the infinite system
C
= 4
π a
is just the limit of the capacitance of the
finite geometry as the outer radius
b
goes to
∞
C
= 4
π
ab
b

a
.
Given that at time
t
= 0
, the conducting sphere with radius
r
=
a
holds an electric charge of 20
π
μ
C
that is uniformly distributed on the surface of the sphere, calculate the following.
a) Given that
C
= 4
π a
compute the capacitance and conductance of the single spherical shell.
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 Spring '08
 Kim
 Electromagnet, 1 km, Electric charge, FY, 1 m

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