Question

Define the coefficient of mutual inductance. Give its unit and dimensional formula.

Answer 1

Hint The above problem is based on the concept of the electromagnetic induction. The electromagnetic induction is the phenomenon in which the emf induced in an object due to variation in flow of current in another object. This phenomenon depends on the medium between the both objects, current and number of turns in the coil.

Complete step by step answer
When the current flows in a coil then a magnetic field produces in the vicinity of the coil. The magnetic field of the current carrying coil creates a magnetic flux in the other coil placed at some distance. The variation in the current in the first coil causes the change in the magnetic flux in other coils. The change in magnetic flux induces an emf in another coil and current starts flowing in another coil called the induced current. Similarly, the change in current of other coils induces an emf in the first coil. This property of the coil to induce the emf in the coils is called the mutual inductance. The mutual inductance is also the same as the ratio of the induced emf to per unit current change in the coil.
The expression of the mutual inductance is given as,
$M = \dfrac{{N\phi }}{I}$
Here, N is the number of turns in the other coil, $\phi $ is the magnetic flux in the other coil due to the magnetic field of the first coil, I is the current in the first coil.
The unit of the mutual inductance is Henry and dimensional formula of the mutual inductance is $\left[ {{\text{M}}{{\text{L}}^2}{{\text{T}}^{ - 2}}{{\text{A}}^{ - 2}}} \right]$.

Note The transformers work on the principle of the mutual inductance. The mutual inductance is independent from the size of the coil and only depends on the size of the current carrying coil. If the medium between the coils is more permeable then the value of the mutual inductance also becomes high.