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Electricity and Magnetism I (P331)
Homework 3
Due: Wednesday, September 23, 4:00 PM
The ﬁrst exam will be
Friday, September 25
in class. It will cover primarily Chapter 2 in the Griﬃths
text. Chapter 1 contains necessary mathematical background.
1. Imagine a spherical
shell
of radius
a
and charge
Q
. Suppose a small circular patch with radius
b
is
removed from the shell. (Assume that
b
±
a
.) Show that the magnitude of electric ﬁeld inside of this
hole at a radius
a
is
Q/
(8
π±
0
a
2
).
2. Consider a spherical
shell
of radius
R
and charge
Q
. Show that the net force exerted on the top half
of the shell by the bottom half of the shell is
Q
2
/
(32
π±
0
R
2
). Be careful what value you use for the
electric ﬁeld in the computation! (Read Section 2.5.3.)
3. A sphere of radius
R
carries a charge density
ρ
(
r
) =
kr
2
(where
k
is constant). Find the energy of
this charge conﬁguration. There are two diﬀerent ways to get the solution (Eqs. 2.43 and 2.45) – do
it both ways and show they produce the same result.
4. (a) Show that the electrostatic energy of a uniformly charged solid sphere, with total charge
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This note was uploaded on 01/20/2012 for the course PHYSICS 331 taught by Professor Staff during the Fall '09 term at Indiana.
 Fall '09
 STAFF
 Magnetism, Work

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