Generators and motors

Generators and motors are applications of electromagnetic induction. Figure 2illustrates a simple electric generator. 

Figure 2 A simple electric generator.

The crank represents a mechanical method of turning the loop of wire in a magnetic field. The change in magnetic flux through the loop generates an induced current; thus, the generator converts mechanical energy into electrical energy. The operation of a motor is similar to that of a generator but in reverse. The motor has similar physical components except that the electric current supplied to the loop exerts a torque, which turns the loop. The motor, therefore, converts electrical energy into mechanical energy.

Mutual inductance and self-inductance

Mutual inductance occurs when two circuits are arranged so that the change in current in one causes an emf to be induced in the other.

Imagine a simple circuit of a switch, a coil, and a battery. When the switch is closed, the current through the coil sets up a magnetic field. As the current is increasing, the magnetic flux through the coil is also changing. This changing magnetic flux generates an emf opposing that of the battery. This effect occurs only while the current is either increasing to its steady state value immediately after the switch is closed or decreasing to zero when the switch is opened. This effect is called self-inductance. The proportional constant between the self-induced emf and the time rate of change of the current is called inductance (L) and is given by 

The SI unit for inductance is the henry, and 1 henry = 1(Vs/A).

Using Faraday's law, inductance can be expressed in terms of the change of flux and current: 

Electromagnetic Induction problems

Faraday’s Law

1. (a) A coil of radius 20 cm consisting of 20 turns is held 2 meters above the south

end of a magnet. If the coil is dropped, determine the average induced EMF

(voltage) once the loop hits the magnet if the field strength at the 2 m height

is 0.005 T, and is 0.01 T at the surface of the magnet.

(b) What is the direction of the induced current, as seen from above the coil?

2..

A square loop of copper coil 10 cm on each side is in static magnetic field of

0.005 T perpendicular to the loop. The coil is deformed into a circle having the

same circumference as the square loop. If this shape-change occurs in 5 seconds,

and the coil has a resistance of 1 , determine the induced current in the coil.

3. A 100 turn conducting circular coil of radius 1 cm is placed in a magnetic field

of variable.

3. A 100 turn conducting circular coil of radius 1 cm is placed in a magnetic field

of variable strength B(t) = 0.01t + 0.01 Tesla, which is perpendicular to the

plane of the loop. Determine the induced EMF.

Lenz’s Law

When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity or direction of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it.

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