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Figure 31.23
(Quick Quiz 31.5) In an old-fashioned equal-arm balance, an aluminum sheet
hangs between the poles of a magnet.
Chapter 31
Faraday's Law
Summary
Concepts and Principles
Faraday’s law of induction states that the emf induced in
a loop is directly proportional to the time rate of change of
magnetic flux through the loop, or
S
S
e 5 2 ddtFB
(31.1)
When a conducting bar of length , moves at a
S
S
velocity S
v through a magnetic field B, where B is
S
perpendicular to the bar and to v, the motional
emf induced in the bar is
e 5 2B,v
(31.5)
where FB 5 e B ? d A is the magnetic flux through the loop.
Lenz’s law states that the induced
current and induced emf in a conductor are in such a direction as to set
up a magnetic field that opposes the
change that produced them.
Objective Questions
A general form of Faraday’s law of induction is
d FB
S
S
C E ? d s 5 2 dt
S
(31.9)
where E is the nonconservative electric field that is produced by the
changing magnetic flux.
1. denotes answer available in Student Solutions Manual/Study Guide
1. Figure OQ31.1 is a graph of the magnetic flux through
a certain coil of wire as a function of time during an
interval while the radius of the coil is increased, the
coil is rotated through 1.5 revolutions, and the external source of the magnetic field is turned off, in that
order. Rank the emf induced in the coil at the instants
marked A through E from the largest positive value to
the largest-magnitude negative value. In your ranking,
!B
A
B
C
D
Figure OQ31.1
E
t