Induced emf. - Lenz's Law

Lenz's law states that whenever the magnetic flux linking an electric circuit undergoes a change an emf is induced in that circuit which is proportional to the time rate at which the flux changes, i.e.

[3-49]

The polarity of this induced voltage is such that if the circuit were closed a current would result and flow in a direction that would oppose any change in the flux.

For example, if the current in the toroid of Fig. 3-9(a) is in the direction shown and is increasing, then the flux would be increasing also. According to Lenz's law the induced emf would be in a direction such as to prevent the flux from increasing, and if the induced emf were acting by itself it would produce a current in a direction opposite to that shown in Fig. 3-9(a). This would make the upper terminal positive as marked.

If we were to pass a current i through the winding on the toroid of Fig. 3-9(a) the applied voltage v must be sufficient not only to overcome the resistance drop of the winding but also to overcome the induced emf, and we would have

[3-50]

where R is the resistance of the winding.

In the case of the toroid, if the winding has a large number of turns and the turns are uniformly distributed, then all the turns are linked by the same value of flux, Φ, and Eq. 3-50 may be written as

[3-51]

where N is the number of turns in the winding.