411 Problem Set 3 Spring 09
1.
The capacitance is determined from the definition
C
=
Q
/
Δ
V
,where
Q
is the magnitude
of the charge stored and
Δ
V
is the magnitude of the electrostatic potential difference between
the two surfaces which form the capacitor.
(
a
) In each of the following find
(
r
)
or
E
(
r
)
between the two surfaces and determine the
capacitance in Gaussian units starting from the definition
C
=
Q
/
Δ
V
. Use Gauss’ law to find
E
, if needed.
i). parallel plate capacitor, area
A
, plate separation
d
(
d
<<
A
)
ii). length, L, of a long cylindrical capacitor, inner radius
a
, outer radius
b
;
iii). a solid spherical conductor with radius,
R
.
(
b
) Show in each case that the total electrostatic energy,
W
=
1
8
∫∫∫
∇
(
r
)
2
d
3
x
,
stored in the field (note the integral is over all space) is given by
1
2
QV
Jackson problem 1.10
For a charge free space prove that the value of the potential at any point is equal to the
average of the potential on any spherical surface centered on the point.
Jackson problem 1.14(revised)
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 Spring '10
 G
 Charge, Electrostatics, Energy, Laplace, Electric charge, Fundamental physics concepts

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