The mutual inductance of a pair of coils does not depend on

The correct answer is Option (4) → the material of the coil

Mutual inductance is the flux linked with one coil per unit current in the other, \( N_2\phi_2 = MI_1 \). It is therefore decided by how much of the field of one coil passes through the other: the size, shape and number of turns of the coils, their separation, their relative orientation, and the permeability of the medium (core) between them. For two long coaxial solenoids, for example:

    \( \displaystyle M = \frac{\mu_0 N_1 N_2 A}{l} \)

The material of the wire the coils are wound from (copper, aluminium, etc.) changes their resistance but not the magnetic flux linkage, so M does not depend on it.

Note: The question does not say which material is meant. It is taken here as the material of the wire the coils are wound from, which gives the answer given by NTA. If it is read as the material of a core inside the coils, the mutual inductance does depend on it through the core’s permeability, and none of the options would then be correct.

NCERT (2026-27):
Mutual Inductance – “… We explained the above example with air as the medium within the solenoids. Instead, if a medium of relative permeability \( \mu_r \) had been present, the mutual inductance would be

    \( M = \mu_r\,\mu_0\,n_1 n_2\,\pi r_1^{2}\,l \)

It is also important to know that the mutual inductance of a pair of coils, solenoids, etc., depends on their separation as well as their relative orientation.”