Question

The mutual inductance of a pair of coils, each of N turn, be M henry. If a current of i ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt will be
A. $\dfrac{{Mi}}{t}$
B. $\dfrac{{NMi}}{t}$
C. $\dfrac{{MN}}{{it}}$
D. $\dfrac{{Mi}}{{Nt}}$

Answer 1

Hint: When two coils are brought in the vicinity of each other the magnetic field in one of the coils tend to link with the other. Which further leads to the generation of voltage in the second coil. This property of a coil which affects or changes the current and voltage in a secondary coil is known as mutual inductance.
Formula Used: $E = - M\dfrac{{dI}}{{dt}}$

Complete answer:
Induction is defined as the magnetic field which is proportional to the rate of change of the magnetic field. Induction is also known as inductance. Inductance is expressed as ‘L’ and its SI unit is Henry.
Induction is further classified in two types, self-induction and mutual induction.
When there occurs a change in the current or magnetic flux of the coil, an opposing induced electromotive force is produced, this phenomenon is known as Self Induction.
Mathematically it is given as, $E = - L\dfrac{{dI}}{{dt}}$
When the current in one coil induces emf in the other coil is defined as the Mutual inductance. Mathematically, mutual inductance ${M_{21}}$ of coil 2 with respect to coil 1 is given by,
$\eqalign{
  & \phi = I \cr
  & \Rightarrow \phi = MI \cr} $
Where ‘M’ is expressed as the mutual inductance of the two coils.
Now, the rate of change of magnetic flux in the coil is given as,
$\eqalign{
  & E = - \dfrac{{d\phi }}{{dt}} = - \dfrac{{d\left( {MI} \right)}}{{dt}} \cr
  & \Rightarrow E = - M\dfrac{{dI}}{{dt}} \cr} $
Now, using the above relation of mutual inductance and the rate of change of magnetic flux in the coil we can solve the given question.
So, according to the given question,
$\eqalign{
  & E = \dfrac{d}{{dt}}\left( {NMi} \right) \cr
  & \Rightarrow E = NM\dfrac{{di}}{{dt}} \cr
  & \therefore E = \dfrac{{NMi}}{t} \cr} $
Thus, emf induced per unit turn in the other coil in volt will be $\dfrac{{NMi}}{t}$.

Hence, option (B) is the correct answer.

Note:
The principle difference between the self-induction and mutual induction is that, self-induction is the characteristic of the coil itself whereas mutual inductance is the characteristic of the pair of coils.