Physics Project Report on Electromagnetic Induction :
Electromagnetic Induction (EMI) : In 1831 Michael Faraday discovered the effect called “Electromagnetic Induction” just converse to the magnetic effect of electric current.
When a coil made of copper wire is placed inside a magnetic field, magnetic flux is linked with the coil. Faraday found that when the magnetic flux linked with the coil is changed, an electric current starts flowing in the coil, provided the coil is closed one. The current and e.m.f. so produced are called induced current and induced e.m.f. The induced current and the e.m.f. in the coil last only so long as the magnetic flux linked with the coil keeps on changing.
Thus electromagnetic induction is the phenomenon of production of electric current (or e.m.f.) in a coil when the magnetic flux linked with the coil is changed.
The following experiment performed by Faraday led to the discovery of the electromagnetic induction.
When the strength of magnetic field is varied :
Consider two coil P and S wound on an iron rod. Iron rod is connected with galvanometer, battery and tapping key. When tapping key is pressed and when it is released galvanometer shows deflection showing the presence of induced current.
Explanation : When the tapping key is pressed then magnetic flux linked with the coil S changed because of increase in magnetic field of coil P and induced current is produced and when it is released magnetic flux is again changed and induced current is produced. But when the tapping key is kept pressed then the magnetic flux linked with coil do not changed and induced current do not produce so galvanometer shows no deflection.
Faraday’s Laws of Electromagnetic Induction :
The results of Faraday’s experiment on electromagnetic induction are known as “Faraday’s Law of Electromagnetic Induction”. These are stated as below :
1. Whenever magnetic flux linked with a circuit (a loop of wire or a coil or an electric circuit in general) changes, induced e.m.f. is produced.
2. The induced e.m.f. lasts as long as the change in magnetic flux continuous.
3. The magnitude of induced e.m.f. is directly proportional to the rate of change of magnetic flux linked with the circuit.
Lenz’s Rule :
Lenz’s rule is a convenient method to determine the direction of induced current produced in the circuit.
Lenz’s law states that the induced current produced in a circuit always flows in such a direction that it opposes the change or cause that produce it.
Let us now apply Lenz’s law to find the direction of flow of induced current in the circuit.
On pressing the key the current in the coil P flows in clockwise direction and magnetic lines of force are directed from left to right. Then magnetic flux linked with the coil S changed. The direction of induced current should be such that it should oppose the direction of flow of magnetic field lines. So induced current in the coil S is in the direction opposite to the magnetic field in P. Hence, direction of induced current in coil S is from right to left. So induced current in coil S should flow in anticlockwise direction.
Expression for Motional e.m.f. :
Consider that a uniform magnetic field B confined to the region PQRS and a coil ABCD is placed inside the magnetic field. The direction of magnetic field is perpendicular to the plane of the coil and in inward direction.
Consider that at any time t, the part BA’ = CD’ = x(say) of the coil inside the magnetic field. If l is the length of the arm BC of the coil, then area of coil inside the magnetic field at any time t.
A = BCX CD’ = lx
Therefore magnetic flux linked with the coil at any time t.
f = BA = Blx
Suppose that the coil is pulled out of the magnetic field with velocity n. As the coil is pulled out magnetic flux linked with the coil changes. The time rate of change of magnetic flux linked with the coil is given by
If e is induced e.m.f. produced, then
e = -Bln
The negative sign shows that induced e.m.f. opposes to the coil being pulled out of magnetic field.
Mutual Induction :
Consider two coil P and S are placed very close to each other. Coil P consists of battery and tapping key and coil S consists of galvanometer G. When the key of coil P is pressed then magnetic flux is building and induced e.m.f. produced in it opposes the flow of magnetic flux. Because coil P and coil S are very close to each other. So magnetic flux also changed in coil S and induced current is produced which opposes the direction of flow of magnetic lines of force in coil P.
The phenomenon according to which an opposing e.m.f. is produced in a coil as a result of change in current or magnetic flux linked with a neighboring coil is called mutual induction.
Coefficient of Mutual Induction :
Suppose that current I is flowing through coil P and f be the magnetic flux linked with coil S
f a I
f = MI
M = Coefficient of mutual induction.
Let e be the induced e.m.f. in coil S.
e = – (-ive sign shows opposition of induced e.m.f.)
M = e /
The mutual inductance of two coils is said to be one Henry, if a rate of change of current of 1 ampere per second in one coil induces an e.m.f. of 1 volt in neighboring coil.
Consider a coil connected to a battery and a tapping key. When key K is pressed magnetic lines of forces starts growing through it and induced e.m.f. is produced. Direction of induced e.m.f. is opposite to that of growth of current. On the other hand when key is released the current in the coil decreases and e.m.f. is produced in opposite direction. Thus during both growth and decay of current an opposite induced e.m.f. is produced. This e.m.f. is called back e.m.f.
The phenomenon according to which an opposing induced e.m.f. is produced in the coil as a result of change in current or magnetic flux linked with the coil is called self induction.
Coefficient of Self Induction :
Suppose when key is pressed, current I flows through the coil and magnetic flux f linked with the coil.
f a I
f = MI
L is called coefficient of self induction.
Let e be the induced e.m.f.
e = (-ive sign shows opposing nature of induced e.m.f.)
M = e /
Self inductance of a coil is said to be one Henry if a rate of change of current of 1 ampere per second induces an e.m.f. of one volt.
Eddy Currents :
Eddy currents are the currents induced in a conductor, when placed in a changing magnetic field. They are also known as Focaults Currents.
Following experiment explain the origin of eddy currents. Introduce a soft iron core inside a solenoid and connect it to the source of alternating current. Place a metallic disk over soft iron core.
Explanation : When the circuit is switched on the current starts growing and hence magnetic flux linked with disk also increases. Thus disk is converted to small magnet. If soft iron’s upper face acquires north polarity. Then metallic disk’s lower surface acquires north polarity and due to repulsive force metallic disk placed over soft iron core is thrown up into the air.
Application of Eddy Currents :
1. Dead Beat Galvanometers :
The oscillation of a moving coil galvanometer generally take a long time to die out. But by winding its coil on a metallic frame made of copper or aluminium the galvanometer can be made dead beat. It is because, due to production of eddy currents in a metallic frame. The coil of galvanometer comes to rest very soon.
2. Speedometer :
In speedometer, a small magnet is geared to the main shaft of the vehicle. The magnet is mounted in an aluminium cylinder with the help of hair springs. Due to rotation of magnet eddy currents are produced which led the drum to oppose the motion of relating magnet drum experience torque and gets deflected at certain angle.
3. Electric Brakes :
A metallic drum is coupled to the wheels of train ; so that when train rotates drum also rotates. In order to stop the train magnetic field is applied to rotating drum. The eddy currents produced oppose the motion of drum. Since drum is connected to wheels of train, it comes to halt.