ECE 329
Homework 7
Due: October 13, 2009, 5 PM
1. Faraday’s Law states that the emf
E
calculated for any closed loop
C
in 3D space equals the decay
rate

d
Ψ
dt
of magnetic flux
Ψ
≡
B
·
dS
. For a loop
C
with a fixed shape, the emf is
E
=
C
E
·
dl
in
terms of electric field
E
in the reference frame of the loop. In that case, Faraday’s law is written as
C
E
·
dl
=

d
dt
S
B
·
dS
where the line and surface integrals are taken in directions compatible with the right hand rule.
a) What is the emf
E
over any fixed loop
C
in a region where
B
= 0
at all times?
b) What is the emf
E
over any fixed loop
C
in a region where
B
is nonzero but timeindependent?
c) If
B
is timeindependent, can the line integral
12
E
·
dl
calculated in the region between (arbi
trary) fixed points
P
1
and
P
2
depend on the path taken from
P
1
to
P
2
? Explain your reasoning.
d) Can the emf
E
calculated for a moving or deforming loop
C
be nonzero if
B
is nonzero but
timeindependent (i.e., static)? Explain.
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 Spring '08
 Kim
 Electric charge, charge density, Gauss’ Law

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