ECE 329
Homework 3
Due: Sept 16, 2008, 5PM
1.
Faraday’s Law
states that induced emf or circulation
E ≡
±
C
E
·
d
l
calculated around any closed loop
C
in space equals the decay rate of magnetic Fux,
Ψ
B
≡
²
S
B
·
d
S
, through any surface
S
bounded
by the loop — that is,
³
C
E
·
d
l
=

d
dt
´
S
B
·
d
S
for line and surface integrals taken in directions consistent with the right hand rule. Based on this
law:
a) What is the induced emf
E
over any ±xed loop
C
calculated in a region where
B
=0
at all times?
b) Can the emf
E
calculated for a moving or deforming loop
C
be nonzero if
B
±
=0
but constant
in time (i.e., static)? Explain.
c) If
B
is timeindependent, can the line integral
²
12
E
·
d
l
calculated in the region between ±xed
points
P
1
and
P
2
depend on the path taken from
P
1
to
P
2
? Explain your reasoning.
2. ²or
B
=
B
0
(
t
cos(
ωt
)ˆ
x
+ sin(
ωt
)ˆ
z
)
Wb/m
2
, ±nd the induced emf
E
around the following closed
paths:
a) A rectangular path going from
(0
,
0
,
0)
to
(1
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 Spring '08
 FRANKE
 Magnetic Field, Electric charge, Righthand rule, rectangular path

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