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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.


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


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


where N is the number of turns in the winding.

Last Update: 2011-08-01