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188
CHAPTER 20
20.33
(a) When a coil having
N
turns and enclosing area
A
rotates at angular frequency
ω
in
a constant magnetic field, the emf induced in the coil is
max
max
sin
where
tN
B
A
⊥
==
EE
E
55.0 T
B
Here,
is the magnitude of the magnetic field perpendicular to the rotation axis of
the coil. In the given case,
B
⊥
µ
⊥
=
;
A
ab
π
=
where
( )
10.0 cm
2
a
=
and
( )
4.
b
=
00 cm
2; and
rev
1 m
100
1
min
60.0
()
in
0.5
s
=
2
ωπ
2
rad s
f
Thus,
6
10.0
55.0
10
T
0.040 0 m
10.5 rad s
4
−
=×
max
E
0.100 m
or
5
1.81
10
V
18.1 V
max
−
=
E
(b) When the rotation axis is parallel to the field, then
0
B
⊥
=
giving
max
0
=
E
It is easily understood that the induced emf is always zero in this case if you
recognize that the magnetic field lines are always parallel to the plane of the coil,
and the flux through the coil has a constant value of zero.

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