Page 351 - Schaum's Outline of Theory and Problems of Applied Physics

336 ELECTROMAGNETIC INDUCTION [CHAP. 28

B

N turns

Cross-sectional area A
Fig. 28-2

symbol (Greek capital letter phi):

= BA
Magnetic flux = (magnetic field)(cross-sectional area)

2
The unit of magnetic flux is the weber (Wb), where 1 Wb = 1T·m . According to Faraday’s law of electromag-
netic induction, the emf induced in the coil when the magnetic flux through it changes by in the time t is
given by

Induced emf = V =−N
t

LENZ’S LAW

The minus sign in Faraday’s law is a consequence of Lenz’s law: An induced current is always in such a direction
that its own magnetic field acts to oppose the effect that created it. For example, if B is decreasing in magnitude in
the situation of Fig. 28-2, the induced current in the coil will be counterclockwise in order that its own magnetic
field will add to B and so reduce the rate at which B is decreasing. Similarly, if B is increasing, the induced
current in the coil will be clockwise so that its own magnetic field will subtract from B and thus reduce the rate
at which B is increasing.

SOLVED PROBLEM 28.1
The vertical component of the earth’s magnetic field in a certain region is 3×10 −5 T. What is the potential
difference between the rear wheels of a car, which are 1.5 m apart, when the car’s velocity is 20 m/s?
The rear axle of the car may be considered as a rod 1.5 m long moving perpendicular to the magnetic field’s
vertical component. The potential difference between the wheels is therefore

V = Blv = (3 × 10 −5 T)(1.5m)(20 m/s) = 9 × 10 −4 V = 0.9mV

SOLVED PROBLEM 28.2

A square wire loop 8 cm on a side is perpendicular to a magnetic field of 5 × 10 −3 T. (a) What is the
magnetic flux through the loop? (b) If the field drops to 0 in 0.1 s, what average emf is induced in the
loop during this time?
(a) The area of the loop is
(8cm)(8cm) 2 −3 2
A = = 0.0064 m = 6.4 × 10 m
(100 cm/m) 2