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ELE401  Field Theory: Tutorial Problems
Week 6
1. Develop the expression for
C
the capacitance for the following geometries
by assuming a charge +
Q
on one surface and

Q
on the other conducting
surface.
(a) Figure 1 shows a concentric conducting cylinders with an inner radius
ρ
=
a
and an outer cylinder radius
ρ
=
b
. Assume inner cylinder
carries +
Q
[
C
] of charge, therefore the outer one has

Q
[
C
]. Develop
the expression for
C
by
i. Solving for
~
D
then
~
E
ii. Next develop
V
ab
iii. Finally
C
=
Q
V
ab
x
y
z
L
a
b
Material between
has
Figure 1: A concentric conducting cylinders
(b) Figure 2 shows the cross section of concentric conducting spheres
(shells). Assume inner shell carries +
Q
[
C
]; then outer carries

Q
[
C
].
Solve for:
i. Solve for
~
D
, then
~
E
ii. Next the Voltage
V
ab
of the shells
1
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View Full Document iii. Finally
C
the capacitance
(c) (1a) may be recalculated if
V
(
a
) =
V
o
and
V
(
b
) = 0.
(d) (1b) can be reworked when the voltage is known i.e.
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This note was uploaded on 04/17/2008 for the course ELE 401 taught by Professor Forgot during the Spring '08 term at Ryerson.
 Spring '08
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