# Statically Induced e.m.f.

The e.m.f. induced by variation of flux is termed as “statically induced e.m.f.”.

Statically induced e.m.f. can be further subdivided as follows:

(i)                           Self-induced e.m.f.

(ii)                        Mutually induced e.m.f.

20.2.1. Self-induced e.m.f. Self-induced e.m.f. is the e.m.f. induced in a coil due to the change of its own flux linked with it. If the current through the coil (Fig. 34) is changed then the flux linked with its own turns will also change which will produce in it, what its called self-induced e.m.f.

The direction of this e.m.f. is given by Lenz’s law (and would be such as to oppose any change of flux which is, in fact, the very cause of its production).

Self-inductance

The property of the coil due to which it opposes any increase or decrease of current or flux through it is known as self-inductance. It is measured in terms of self-induction L (in henry).

Self-induction is sometimes analogously called electromagnetic or electrical inertia.

Co-efficient of self-induction (L) may be found by the following relations:

Eqn. (28) is an energy description of inductance.

Example 28. The field winding of a D.C. electromagnets is wound with 800 turns and has resistance of 400 turns of wire of 2 mm2 cross-section. Calculate the value the self-inductance of the coil. Assume µr = 800.

(Gwalior University)

Solution. Given: A = 2 × 2 = 4 cm2 = 4 × 10-4 m2 ;

N = 400,

l = πd =  π × 0.3 = 0.3  πm ;

µr, (relative permeability) = 800

Example 30. An air cored solenoid has a length of 60 cm and a diameter of 4 cm Calculate its inductance if it has 1000 turns and also find the energy stored if the current rises from zero to 6 A.

(VTU August, 2000)

Solution. Given: l = 60 cm = 0.6 m ;

d = 4 cm = 0.04 m ;

N = 1000 ;

i = 5 – 0 = 5 A

Example 31. If a coil of 200 turns is linked with a flux of 0.01 Wb when carrying current of 10 A, calculate the inductance of the coil. If this current is uniformly reversed in 0.01 second, calculate the induced electromotive force.

Solution, Given: N = 200 ; ɸ = 0.01 Wb,

i = 10 A ;

dt = 0.01 s

Example 32.A coil of 1500 turns carrying a current of 5A produces a flux of 2.5 m Wb. If the current is reversed in 0.2 second, find the average value of e.m.f. induced in the coil. Also find the self-inductance of the coil.

(VTU August, 2001)

Solution. Given: N = 1500 ;

i = 5 A;

ɸ = 2.5 m Wb;

dt = 0.2 S.

Example 33.A direct current of one ampere is passed through a coil of 6000 turns; it produces a flux of 0.1 m Wb. Assuming that whole of this flux threads all the turns, what is the inductance of the coil? What would be the voltage developed across the coil if the current were interrupted in 10-3 second? What is the energy stored in the coil.

Solution. Given: i = 1 A;

N = 6000 ;

ɸ = 0.1 m Wb = 0.1 x 10-3 Wb ;

dt = 10-3 s.

Mutually induced e.m.f. Refer Fig. 35. Production of e.m.f in coil B due to change in current A is called induced e.m.f.

• Consider two coils A and B lying close to each other (Fig. 35). Coil A is joined to a battery, a switch (K) and a variable resistance (R) whereas coil B is connected to a sensitive voltmeter V.
• When current through A is established by closing the switch, its magnetic field is set up and partly links with or threads through the coil B. As the current through A is changed, the flux linked with B is also changed. Hence mutually induced e.m.f. is produced in B where magnitude is given by Faraday’s law and direction by Len’s law.

• Now, if battery is connected to B and the voltmeter across A, then the situation is reversed and now a change of current in B will produce mutually-induced e.m.f. A.

–         From the examples considered above, it is evident that there is no movement of any conductor, the flux variations being brought about by variations in current strength only. Such an e.m.f. induced in one coil by the influence of the other coil is called (statically but) mutually induced e.m.f.

Mutual inductance

Mutual inductance may be defined as the ability of one coil (or circuit) to produce e.m.f. in a nearly coil by induction when the current in the first coil changes. This action being reciprocal, the second coil can also induce an e.m.f. in the first coil when current in the second coil changes. This ability of reciprocal Induction is measured in terms of the coefficient of mutual induction M.

Co-efficient of mutual induction (M) may be found by the following relations: