Chapter 30
30.1
In Fig. 3037, the magnetic flux through the loop increases according to the relation
Φ
B
=
6.0
t
2
+
7.0
t
where the flux is in milliWebers and t is in seconds.
(a)
What is the magnitude
of the emf induced in the loop at t=2.0s?
(b) In what direction will the current flow through the
resistor.
The magnitude of the induced emf is given by
Φ
B
=
6.0
t
2
+
7.0
t
ε
=
d
Φ
B
dt
=
12.0
t
+
7.0
ε
(2)
=
12.0
⋅
2
+
7.0
=
31
mV
The flux is pointing out of the paper and rising.
The coil reacts to oppose this rising outward field
by generating a field that points into the paper.
To do this, the current must flow to the left through
the resistor.
30.3
A small loop of area 6.8
mm
2
is placed inside a long solenoid that has 854 turns/cm and
carries a sinusoidally varying current i of amplitude 1.28 A and angular frequency 212 rad/s.
The
central axis of the loop
and the solenoid coincide.
What is the amplitude of the emf induced in the
loop
The emf generated can be calculated by finding the rate of change of magnetic flux through the
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 Spring '07
 Ndili
 Magnetic Field, loop, uniform magnetic field

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