Question

Lenz’s law is expressed by the following formula (here, e=induced e.m.f., \[\phi \]=magnetic flux in one turn and N=number of turns)
A. \[e = - \phi \dfrac{{dN}}{{dt}}\]
B. \[e = - N\dfrac{{d\phi }}{{dt}}\]
C. \[e = - \dfrac{d}{{dt}}\left( {\dfrac{\phi }{N}} \right)\]
D. \[e = N\dfrac{{d\phi }}{{dt}}\]

Answer 1

Hint: Recall the statement for Lenz’s law. From this statement of Lenz’s law, determine the mathematical expression for induced emf in one turn of the loop. Then write this mathematical expression of induced emf in the loop for N turns of the loop.

Complete step by step answer:
Lenz’s law states that the electromotive force induced in a loop gives the rise to electric current and the magnetic field produced by this electric current will oppose the change in the magnetic flux linked loop and tries to maintain the original magnetic flux linked with the loop to the same value.

Hence, the mathematical expression for induced emf \[e\] is
\[e = - \dfrac{{d\phi }}{{dt}}\]
Here, \[\phi \] is the magnetic flux linked with one turn.
The total emf \[{\phi _T}\] of the loop for N turns is
\[{\phi _T} = N\phi \]
Thus, the induced emf for the for N turns of the loop is given by
\[\therefore e = - N\dfrac{{d\phi }}{{dt}}\]
This is the required expression for induced emf according to Lenz’s law.

Hence, the correct option is B.

Additional information:
The Lenz’s law is dependent on Newton’s third law of motion and law of conservation of energy. It is used to determine the direction of induced emf. The direction of the induced current is always in a direction such that it opposes the change in magnetic field linked with it.

Note: The students should not forget to use the negative sign in the mathematical expression for induced emf in the loop. Because this negative sign indicates that the electric current produced in the loop opposes the change in magnetic flux linked with the loop. Hence, the mathematical expression without this negative sign will not be correct.