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Chapter 31
Faraday’s Law of Induction
Objectives:
1. To understand how a current is created when a rectangular loop of wire moves
through a magnetic field.
2. To understand the meaning of flux:
   B dA
3. To understand the source and meaning of Faraday’s law:
 
d
dt
4. To understand how to use Lentz’s law to determine the direction of current.
5. To understand how to calculate the amount of induced current in a loop of wire when
the flux through the loop is changing.
6. To understand how to obtain the electric field (magnitude and direction) created by a
changing magnetic field:
 E ds  
d
dt
Chapter 31 Problems
1.
A square wire loop 3 m on a side lies at right angles to a uniform magnetic field of 2
T. A 6 V bulb is in series with the loop. The magnetic field is decreased steadily to
zero over a time interval t. How long must t be if the light is to shine at full
brightness during this time?
B
2.
A pair of parallel conducting rails lie in a uniform magnetic field B pointing into the
page. The rails are a distance L apart and a resistance R is connected to them. A bar
lying across the rails is being pulled to the right with a constant speed v. (a) What is
the direction and magnitude of the current is the resistor? (b) At what rate must
work be done by the agent pulling the bar?
B
R
v
3.
A solenoid 2 m long and 30 cm in diameter consists of 5000 turns of wire. A 5 turn
wire loop is wrapped around the outside of the solenoid. A 180  resistor is
connected to the 5 turn loop. The current in the solenoid is reduced steadily from 40
A to zero over a time of 10 ms. During this time, what is the magnitude of the
current in the resistor?
4.
A car alternator consists of a 250 turn wire loop of diameter 10 cm. The magnetic
field in the alternator is .1 T. If the alternator is turning at 1000 revolutions per
minute, what is the peak output voltage?
B
5.
The plasma in a tokamak is heated in part by the current driven by the induced
electric field. The magnetic field B in the center of a tokamak is provided by coils
(not shown in picture). This field is confined to a circular area of radius 50 cm. (a)
If the magnetic field changes at the rate of 5100 T/s, what is the induced electric field
1.2 m from the center of the tokamak? (b) If a proton located 1.2 m from the center
were to circle the tokamak twice during the time the field was changing, how much
energy would it gain?
B
1.2 m