Electromagnetic Induction

Magnetic flux f  :   f = B A cos θ   and              Flux-linkage =

 Faraday's law of electromagnetic induction

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

or rate of flux-cutting

Lenz's law

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

1.      E.m.f. induced in a straight conductor :  ε  =  B L v

2.      E.m.f. induced between the centre and the rim of a spinning disc :

      ε = B πr²f

       3.    E.m.f. induced in a rotating coil :          ε  = N A B w sin wt

d.c. motors  :          V - E_b = I r    and             V I = E_b I + I r²

Power supplied to the motor = mechanical power output of the motor + power dissipated as heat in the armature coil

Self-induction

             and                  

Energy stored in an inductor  :   

Transformers  :       

( Experiment I )     ( Experiment II )

Explanation of experiment I and II

When a great load ( or smaller resistance ) is connected to the secondary coil, the flux in the core decreases. The e.m.f., ε_p,  in the primary coil falls. 

V_p - ε_{p = I R          and}                

The L R ( d.c. ) circuit  :    or    

1.  The current flowing through the inductor L decreases or increases exponentially and does not change suddenly.