Magnetism & Electromagnetic Induction
Induced Electromotive Force
A changing magnetic field can induce a current in a circuit. The driving force behind the current is referred to as the induced electromotive force.
An induced current occurs when there is a change in the magnetic field. The magnitude of the induced current depends on the rate of change of the magnetic field.
Flux is the amount of field passing perpendicularly through an area multiplied by that area.
Definition
of Magnetic Flux, 
(10) 
Units:
Example 12
A rectangular
coil of wire is situated in a constant magnetic field whose magnitude
is 0.50 T. The coil has an area of 
.
Determine the magnetic flux for the three orientations, 0°, 60.0°,
and 90.0° as shown in the figure.
Faraday's Law of Electromagnetic Induction
The average emf 
induced
in a coil of N loops is
(11) 
Units: V
Example 13
A coil of wire
consists of 20 turns, or loops, each of which has an area of . A magnetic
field is perpendicular to the surface of each loop at all times, so
that 
.
At time 
,
the magnitude of the field at the location of the coil is 
.
At a later time t = 0.10 s, the magnitude of the field at the coil
increased to B = 0.060 T. (a) Find the average emf
induced in the coil during this time. (b) What would
be the value of the average induced emf if the magnitude of the magnetic
field decreased from 0.060 T to 0.050 T in 0.10 s?
Lenz's Law
The induced emf resulting from a changing magnetic flux has a polarity that leads to an induced current whose direction is such that the induced magnetic field opposes the original flux.
Determining the Polarity of the Induced Emf
1. Determine whether the magnetic flux that penetrates a coil is increasing or decreasing.
2. Find what the direction of the induced magnetic field must be so that it can oppose the change in flux by adding to or substracting from the original field.
3. Having found the direction of the induced magnetic field, use the Right-Hand-Rule to determine the direction of the current. Then the polarity of the induced emf can be assigned because conventional current is directed out of the positive terminal, through the external circuit, and into the negative terminal.
