#### Electromagnetic Induction, Physics tutorial

Introduction:

We are familiar that an electric current makes a magnetic field. The reverse effect of generating electricity through magnetism was introduced independently in the year 1831 by Faraday in England and Henry in America and is termed as electromagnetic induction. Certainly, the growth of electrical engineering as we are familiar with it today started with Faraday and Henry who independently introduced the principles of induced e.m.f and the methods through which mechanical energy can be transformed or changed directly to electrical energy. You would realize that out present day large scale production and distribution of electrical energy would not be reasonably feasible if the mere sources of e.m.f. available were those of the chemical nature, like dry cells.

Electric Field accompanying a time - Varying Magnetic Field:

In an area where a magnetic field is changing, there is an electric field that is associated to the time rate of change of the magnetic field.

The basic relationship between the electric field 'E' and the time rate of change ∂B/∂t of the magnetic field that is deduced from the outcomes of a number of experiments in Faraday's law:

cEs ds = - ∫S(∂BN/∂t) dA

Here 'S' is any (open) surface bounded through an arbitrary closed curve 'C'. 'BN' is the component of 'B' all along the normal n to S, where the direction of n is associated to the positive direction for the path of integration 'C'.

We examine that Faraday's law means that the basic relationship of electrostatics:

cEs ds = 0

is true if and only if B is not time-dependent.

The surface integral in Faraday's law can be interpreted in terms of the magnetic flux included by C:

Φ = ∫SBN dA

The rate of charge of this flux related with time variations of 'B' is:

∂Φ/∂t = ∂/∂t ∫SBN dA = ∫S ∂BN/∂t dA

Thus, the Faraday's law can be written as:

Φc Es ds = - ∂Φ/∂t

Induced e.m.f. and Currents:

The Induced e.m.f. can be produced in two manners.

1) By relative movement (the dynamo effect):

When a bar magnet is moved into and out of a stationary coil of wire joined to a centre - zero galvanometer, a small current is recorded throughout the motion however not at other times. Movement of the coil in the direction or away from the stationary magnet consists of similar results. The relative motion between the coil and magnet is essential.

Observation exhibits that the direction of the induced current based on the direction of relative motion. As well the magnitude of the current rises with the speed of motion, the number of turns on the coil and the strength of the magnet.

You must note that however it is current we detect in this explanation, an e.m.f should be induced in the coil to cause the current. The induced e.m.f is more fundamental quantity and is for all time present even if the coil is not in a complete circuit. The value of induced current based on the resistance of the circuit and also on the induced e.m.f.

2) By Changing a Magnetic Field (the transformer effect):

In this situation, the two coils are arranged close to each other. It is noticed that a transient current is induced when:

a) Steady current in the adjacent circuit is turned on or off.

b) The adjacent circuit having a steady current is moved relative to the first circuit.

This is worth noting that the induced current is in one direction if the current in the first coil rise and in the opposite direction if it reduces.

Cases of electromagnetic induction in which the current changes in one circuit cause induced e.m.f in a neighboring circuit, not joined to the first, are illustrations of mutual induction - the transformer principle.

The induced e.m.f is directly proportional to the rate of change of the flux linkage.

In calculus notation, it can be represented as:

E α d/dt (NΦ)

Or E = constant x (d/dt) (NΦ)

Here 'E' is the induced e.m.f and d(NΦ)/dt is the rate of change of flux linkage. The law is found to be true for the dynamo and the transformer kinds of induction.

There are additional experimental examinations which are concerned by the properties of coil itself that influence the e.m.f. induced in it. They will assist you further with the understanding of Faraday's law.

• Number of turns, N
• Area, A
• Orientation θ

Lenz's Law:

As the magnitude of the induced e.m.f. is introduced by Faraday's law, its direction can be finding out by a law due to the Russian Scientist Lenz. It might be stated as follows.

The direction of the induced e.m.f. is such that it tends to oppose the flux-change causing it and does oppose it when induced current flows.

Therefore in the figure above a bar magnet is represented approaching the end of a coil, North Pole first. If Lenz's law applies, then the induced current must flow in a direction that makes the coil behave similar to a magnet having a north pole at the top. The downward motion of the magnet and the accompanying flux linkage will then be opposed. If the magnet is withdrawn, the top of the coil must behave similar to a south pole, and attract the north pole of the magnet, therefore hindering its elimination and again opposing the flux-change. The induced current is thus in the opposite direction to that if the magnet approaches.

For straight conductors moving at the right angles to a magnetic field a more helpful version of Lenz's law is Fleming's right-hand rule (as well termed as the dynamo rule; his left-hand rule is frequently termed to as the motor rule).

Fleming's right-hand rule:

Fleming's right hand rule define that if the thumb and the first two fingers of the right hand are held so that each is at right angles to the other by the first finger pointing in the direction of the Field and the thumb in the direction of the motion of the conductor, then the second finger points out the direction (that is, conventional) of the induced current.

Lenz's law is incorporated in the mathematical expression of Faraday law by comprising a negative sign to represent that Current due to the induced e.m.f generates an opposing flux-change, therefore we write:

E = d/dt (NΦ)

Generators (a.c and d.c):

An electrical generator is a machine or device which produces electricity from mechanical energy, generally through electromagnetic induction. The Electromagnetic induction works forcibly by moving a loop of wire (that is, a rotor) around a stationary bar (that is, a stator) which gives an electric field, either via a permanent magnet or an electromagnet. By using the Faraday's law, this induces a current in the rotor that can be employed to power machinery or charge batteries. The possible sources of mechanical energy comprise steam engines, water falling via a turbine or water-wheel, an internal combustion engine, a hand crank, a wind turbine, solar energy, compressed air and loads of others. The electrical generator is the base of our modern electrical society. If electrical generators were to stop operating, so would the majority of the economy.

The electrical generator was first introduced by the Hungarian inventor and engineer Anyos Jedlik between 1827 and 1830. Jedlik discovered the generator, a simple dynamo, at least six years before Warner von Siemens in Germany and Charles Wheatstone in Britain, whose names are generally related with the device's invention.

There are two kinds of generators, one is ac generator and the other is dc generator. Whatever might be the kinds of generators, it for all time transforms mechanical power to electrical power. An ac generator generates alternating power. A DC generator generates direct power. Both of such generators generate electrical power, based on the similar basic principle of Faraday's law of electromagnetic induction. According to this law, if a conductor moves in the magnetic field it cuts the magnetic lines force, due to which an emf is induced in the conductor. The magnitude of such induced emf based on the rate of change of flux (that is, magnetic line force) linkage by the conductor. This emf will cause a current to flow when the conductor circuit is closed.

DC generator:

An electrical Generator is a machine that changes mechanical energy (or power) into electrical energy (or power).

Principle: It is mainly based on the principle of production of dynamically (or motionally) induced e.m.f (that is, Electromotive Force). If a conductor cuts magnetic flux, dynamically induced e.m.f. is generated in it according to the Faraday's Laws of Electromagnetic Induction. This e.m.f. causes a current to flow when the conductor circuit is closed.

Therefore, the fundamental necessary parts of an electric generator are:

• A magnetic field.
• A conductor or conductors that can so move as to cut the flux.

AC generator:

The A.C. generators or alternators (as they are generally termed) operate on similar basic principles of electromagnetic induction as D.C. generators.

Alternating voltage might be produced by rotating a coil in the magnetic field or by rotating a magnetic field in a stationary coil. The value of the voltage generated based on:

• The number of turns in the coil.
• Strength of the field.
• Speed at which the coil or magnetic field rotates.

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