## Electromagnetic Induction

The principles of induction are how we generate electric power. Recording and playback of audio tapes is done with the principle of magnetic induction. Microphones, electric guitars, and other musical instruments use induction. Electric motors and transformers operate by induction.

Voltage can be induced by the relative motion of a wire with respect to a magnetic field. Voltage is induced whether the magnetic field of a magnet moves past a stationary conductor, or the conductor moves through a stationary magnetic field. The results are the same for the same relative motion. The amount of voltage depends on the speed the wire crosses the magnetic field lines.

Electromotive force (EMF) refers to energy per charge or potential. It is not a force but is a potential difference measured in voltage. An EMF and a current is induced in a loop when there is a change in magnetic field in the loop. The magnitude of the induced emf is proportional to the rate of change of the flux. The induced emf in turn sets up a current that itself produces a magnetic field to oppose the change of the the applied magnetic field. Notice, the induced field opposes a change in the magnetic field not the magnetic field itself! This is the reason for the minus sign in the equation. EMF due to a loop of wire being pulled through a magnetic field may be written as

### )M = LI

Remember, stationary charges produce electric fields. Electric currents produce magnetic fields that wrap around the wires according to the right hand rule (see magnetism lesson). If you place a positive charge at rest in an electric field, it moves in the direction of the field. If you place a positive charge at rest in a magnetic field, it moves nowhere. Only a moving electric charge that has a component of its velocity perpendicular to a magnetic fieldexperiences a force. The force is perpendicular to both direction of the charge's velocity and the magnetic field. Moving electric charges are inside a stationary magnet.

According to Faraday's Law if a magnet is passed through a loop of wire connected to a galvanometer, three things are observed:]

1. A current is observed in the loop when the magnet is moving. If the magnet is still, you get nothing.

2. The direction of the current depends on the direction of the magnet. If the magnet moves the opposite way, the direction of the current is reversed.

3. The magnitude of the deflection (current) is proportional to the strength of the magnet and its velocity.

A generator is a device that has a coil which moves in a stationary magnetic field. This is opposite a motor which converts electrical energy into mechanical energy. Generators convert mechanical energy into electrical energy. The voltage induced by the generator alternates, and the current produced is alternating current (AC). The current changes magnitude and direction during 60 Hz. To find the effective voltage or current of an AC generator

### Veff = 0.707Vmax

In a transformer, two coils are used. Instead of a switch to produce the change in magnetic field, an alternating current is used to power the primary coil. It is customary to refer to the coil connected to the power source as the primary (input), and the other as the secondary (output). Voltages may be stepped up or stepped down with transformers. The relationship between primary and secondary coils to the relative number of turns in the coil (N) is:

where V = voltage.

The transformer actually transfers energy from one coil to another. The rate of energy transfer is power. If the slight power loss due to heating of the core are neglected then

### power into primary = power out of secondary

where V = voltage and I = current.

According to Lenz's Law, the duration of the induced current is such that the magnetic effects produced by the current oppose the change in flux that caused the current. It is the change in flux not the flux itself!

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