Electrical Engineering ⇒ Topic : Statically Induced E.M.F.

Statically Induced emf

Statically induced emf or transformer emf does not involve any rotation of the conductor or coil, hence is not associated with energy conversion, it is however associated with energy transfer

The magnitude of this emf can be obtained by Faraday's law  

Statically Induced E.M.F.

If the flux in coil A is varied by varying current by rheostat, the flux linked with coil B also changes. As per Faraday's second law, e.m.f. is induced in coil B and its direction will be given by Lenz's law.

Coil A is connected to a battery V via rheostat Rh as shown in Figure (a). Coil B is connected to a voltmeter V. When the current in coil A will be established, the flux will be produced in coil A and it is varied by varying the current in the coil with the help of the rheostat. This varying flux links with coil B and e.m.f. is induced in coil B. This e.m.f. is called mutually induced e.m.f. In this case, there is no movement of coil B. Similarly, if the connection is reversed, i.e., voltmeter is connected to coil A and battery and rheostat to coil B, the e.m.f. will be produced in coil A.

                                                    Figure (a) Statically induced e.m.f. in coil B due to variation of flux in coil A.

Another type of statically induced e.m.f. is self induced e.m.f. in a coil. This is due to the changes of its own flux in the coil itself due to the change of current flowing through it.

In Figure (b), the current through the coil is changed by the rheostat Rh. The flux linked with the coil also changes that will produce self induced e.m.f. in the coil. The direction of induced e.m.f. in the coil is given by Lenz's law such that it will oppose any change of flux in it. This e.m.f. is also known as opposing or counter e.m.f. on self induced e.m.f.

                                                            figure (b) Statically induced e.m.f. in a single coil.

Statically Induced E.M.F.:-When the conductor is stationary and the field is moving or changing, the e.m.f. induced in the conductor is called statically induced e.m.f. A statically induced e.m.f can be further subdivided

into :

1. Self-induced e.m.f. 2. Mutually induced e.m.f.

1. Self-induced e.m.f. The e.m.f induced in a coil due to the change of its own flux linked with it is called self-induced e.m.f. When a coil is carrying current (See Figure a), a magnetic field is established through the coil. If current in the coil changes, then the flux linking the coil also changes. Hence an e.m.f. (= N d∅/dt) is induced in the coil.This is known as self-induced e.m.f. The direction of this e.m.f. (by Lenz's law) is such so as to oppose the cause producing it, namely the change of current (and hence field) in the coil. The self-induced e.m.f. will persist so long as the current in the coil is changing. The following points are worth noting .

                                                              FIGURE (A)

• When cun-ent in a coil changes, the self-induced e.m.f. opposes the change of current in the coil. This property of the coil is known as its self-inductance or inductance.
• The self-induced e.m.f. (and hence inductance) does not prevent the current from changing ; it serves only to delay the change. Thus after the switch is closed (See Figure a),the current will   rise from zero ampere to its final steady value in some time (a fraction of a second). This delay is due to the self-induced e.m.f. of the coil.

2. Mutually induced e.m.f. The e.ml induced in a coil due to the changing current in the neigh-bouring coil is called mutually induced e.m.f.

    Consider two coils A and B placed adjacent to each other as shown in Figure (b). A part of the magnetic flux produced by coil A passes through or links with coil B. This flux which is common to both the coils A and B is called mutual flux (∅_m). If current in coil A is varied, the mutual flux also varies and hence e.m.f. is induced in both the coils. The e.m.f. induced in coil A is called self-induced e.m.f. as already discussed. The e.m.f. induced in coil B is known as mutually induced e.m.f.

                                                     FIGURE  (B)

The magnitude of mutually induced e.m.f. is given by Faraday's laws i.e. e_M= N_B  d∅_M/dt where N_B is the number of turns of coil B and d∅_M,/dt is the rate of change of mutual flux i.e. flux common to both the coils. The direction of mutually induced e.m.f. (by Lenz's law) is always such so as to oppose the very cause producing it. The cause producing the mutually induced e.m.f. in coil B is the changing mutual flux produced by coil A. Hence the direction of induced current (when the circuit is completed) in coil B will be such that the flux set up by it will oppose the changing mutual flux produced by coil A.

The following points may be noted carefully

 The mutually induced e.m.f. in coil B persists so long as the current in coil A is changing. If current in coil A becomes steady, the mutual flux also becomes steady and mutually induced     e.m.f. drops to zero.

The property of two neigh -bouring coils to induce voltage in one coil due to the change of current in the other is called mutual inductance.