Faraday knew that electrical currents cause magnetic fields. He showed that the inverse is also true, that changing magnetic flux through a conducting loop creates an electrical current in the loop. Faraday’s law of induction states that a changing magnetic flux induces an electromotive force, which creates a current in a wire.



There are two possible sources for induced EMF, according to Faraday's law. The induced EMF is equal to the line integral of the electric field, and it is also equal to the negative time derivative of the integrated magnetic flux.



The magnetic flux through the loop can change in several ways to induce an EMF. If the strength of the magnetic field varies over time, an EMF is induced.



Either a change in the magnetic field or a change in the area of the loop (or both) can induce an EMF. For example, an EMF is induced if the conducting loop rotates or changes size.



An induced EMF also is produced if the conducting loop is moving such that the magnetic flux through the loop changes over time.

Sample questions

1. A conducting loop moves at constant velocity as shown, through a region of constant magnetic field.



Which graph correctly depicts the current induced in the loop? Assume counterclockwise current is positive.





2. Calculate the magnitude of induced current in a circular conducting loop of radius 6.0 cm and resistance of 0.020 ohms. Assume the loop is in a magnetic field perpendicular to the plane of the loop, that changes from 1.0 T to 0.40 T in 1.2 seconds.


3. A conducting loop is halfway into a magnetic field as shown. Suddenly the B field starts to increase. What happens to the loop?



A. It is pushed to the left

B. It is pushed to the right

C. It is pushed upward

D. It is pushed downward

E. It does not move



4. The conducting loop is fixed, but the slide wire with mass m, length l and resistance R is free to fall in a magnetic field with strength B. What is the terminal speed of the slide wire?

Maxwell's theory of EM waves

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James Clerk Maxwell was the first to recognize the inherent symmetry between the electric and magnetic facets of electromagnetic waves. In essence, the electric part of the wave induces the magnetic part, and the magnetic part of the wave induces the electric part. This produces a self-sustaining wave that propagates without relying on charges or currents.

The speed of the EM wave is the speed of light, and depends only on the permittivity constant and the permeability constant. This relationship can be derived by showing that Maxwell's laws obey the wave equation.

Applications of induced currents

Generators:



A generator is fundamentally the opposite of an electric motor. A motor converts electrical energy into mechanical energy, where a generator converts mechanical energy into electrical energy. The mechanical energy can be supplied by an outside source such as wind or water turning an armature.

Transformers:



A transformers uses a pair of coils with different numbers of turns to step up or step down voltage.

When two coils are placed near each other, alternating current in one (the primary, which is the one connected to the power source) induces a changing magnetic field. The second coil is within that field, so it has a current induced in it. If the first coil has fewer loops than the second, the second will experience a higher induced voltage than the first. This is called a step-up transformer.

If the first coil has more loops than the second, the second will experience a lower induced voltage than the first and it is called a step-down transformer. Placing an iron core in the coils will intensify the magnetic field in each.



Metal detectors:



A metal detector uses an alternating current in a transmitter coil to create a magnetic field. Induced currents in a detected piece of metal induce a magnetic field, which alters the field of the receiving coil.