Chapter Eleven : Electromagnetic Induction

Definitions and Basic concepts:

1- electromagnetic induction: It is a phenomenon in which an induceelectromotive force and also an induced current are gnerated in the coil on plunging a magnet into or withdrawing a magnet out of a coil.
2- The presence of a soft iron core inside a coil concentrates the lines of magnetic flux that link with the coil. This in turn increases the induced emf and also the induced current.
3- Faraday's laws for the induced emf: induced emf generated in a coil by electromagnetic induction is proportional to the time rate by which the conductor cuts the lines of magnetic flux and is also proportional to the number of turns of the coil.
4- Lenz's rule: The direction of the induced current generated by induction is such that to oppose the change in magnetic flux producing it.
5- Fleming right hand rule: place the thumb, the pointer and the middle finger (with the rest of the fingers) of the right hand mutually at right angles. If the pointer points in the direction of the magnetic field and the thumb in the direction of motion then the middle finger (with the rest of the fingers) will point in the direction of the induced current.
6- Mutual induction: It is thelectromagnetic interaction between two coils kept close to each other (or one inside the other). An electric current with time varying intensity passing in one coil (primary coil) will produce in the second one (secondary coil) an induced current in a direction such that to oppose the variabtions of the current intensity in the primary coil.
7- Self induction: It is the electromagnetic effect induced in the same coil when the intensity of the current increases or decreases. This effect acts to resist such a change in the intensity of current.
8- Coefficient of self induction: It is measured numerically by the "emf" generated by induction in the coil when the intensity of the current passing through it changes at a rate of 1 A/s.
9- The unit of measuring the self induction (Henry): Is the self induction of a coil in which an emf of 1V is induced when a current passes through it which changes at a rate of 1 A/s
Chapter Eleven : Electromagnetic Induction BR-PHE12-0025

Chapter Eleven : Electromagnetic Induction BR-PHE12-0025

10- The self induction of a coil depends on:
a) its geometry b) its number of turns.
c) the spacing between its turns d) the magnetic permeability of its core.
11- The Dynamo (AC generator): It is advice used to convert the mechanical energy to electric energy (AC current and voltage) when its coil rotates in a magnetic field.
12- The simple dynamo (AC generator) consists of:
a) Field magnet (strong magnet). b) a coil of insulated copper wire suspended between the two poles of the magnet.
b) Two meltallic rings in contact whith two graphite brushes connected to an external cirrcut.
13- Acommutator: (cylinder split into number of insulated segments) is used to obtain a DC current and voltage (DC generator)
14- The alternating current: It is current which changes periodically its intensity and direction with time according to a sinusoidal curve.
15- The electric transformer: It is an electric device used to step up or step downn AC emf through mutual electromagnetic induction.
16- The efficiency of the transformer: It is the ratio between the out put electric energy given in the secondary and that available to the primary.
17- The electric motor: It is an electric device used to convert the electric energy to mechanical energy.

Basic Laws::
1- The induced emf generated in a coil of N turns as a result of time variation of magnetic flux Dj_m linked with the coil in an interval of time is given by the relation:
Chapter Eleven : Electromagnetic Induction BR-PHE12-0026

Chapter Eleven : Electromagnetic Induction BR-PHE12-0026

2- The negative sign indicate that the direction of the induced emf is such that to opposite the cause producing it.
3- The emf induced in a secondary coil due to thtime variation in the lines of magnetic flux resulting from a primary coil linking with the secondary coil in the time interval Dt is given by the relation: Chapter Eleven : Electromagnetic Induction BR-PHE12-0027

Chapter Eleven : Electromagnetic Induction BR-PHE12-0027

4- The emf induced by self induction as a result of the current DI passing through the coil in a time Dt is given by the relation: Chapter Eleven : Electromagnetic Induction BR-PHE12-0028

Chapter Eleven : Electromagnetic Induction BR-PHE12-0028

where L is the coefficient of self induction of coil .
5- The emf induced in a straight wire of length Chapter Eleven : Electromagnetic Induction BR-PHE12-0A27

Chapter Eleven : Electromagnetic Induction BR-PHE12-0A27

moving with a uniform velocity D v making an angle q with the magnetic field of magnetic flux density "B" is given by the relation: Chapter Eleven : Electromagnetic Induction BR-PHE12-0029

Chapter Eleven : Electromagnetic Induction BR-PHE12-0029

6- The emf induced in the dynamo is given by the relation:
Chapter Eleven : Electromagnetic Induction BR-PHE12-0030

when N is the number of turns, B the magnetic flux density, A is the area of the face of the coil, q is the angle confined between v and b and w is the angular velocity given by the relation: Chapter Eleven : Electromagnetic Induction BR-PHE12-0031

Chapter Eleven : Electromagnetic Induction BR-PHE12-0031

7- The emf is maximum when q = 90^o ( sin 90^o= 1)
8- The relation between the effective value of current I_eff and its value I_max is given by :
I_eff= 0.707 I_max.
9- The relation between the two emf in the two coils of the transofrmer is : Chapter Eleven : Electromagnetic Induction BR-PHE12-0032

Chapter Eleven : Electromagnetic Induction BR-PHE12-0032

.
10- The relation between the two currents in the two coils of the trnasformer is: Chapter Eleven : Electromagnetic Induction BR-PHE12-0033

11- The efficiency of the trnsformer is given by the relation:
Chapter Eleven : Electromagnetic Induction BR-PHE12-0034

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