The mutual inductance of a pair of coils placed close to each other depends upon
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Relative position and orientation of the two coils
Mutual inductance is defined by \( N_2\Phi_2 = MI_1 \): it is the flux linkage in one coil per unit current in the other. How much of the flux of one coil passes through the other is fixed by the geometry of the pair (numbers of turns, areas, separation, relative position and orientation) and by the permeability of the medium between them. For two coaxial solenoids, for example,
\( \displaystyle M = \mu_0 n_1 n_2 \pi r_1^{2} l \)
Moving a coil or turning it changes the linked flux, and so changes M.
Why the other options are incorrect
Option (1) The rate at which currents are changing in the two coils. — Incorrect. The rate of change of current decides the induced emf, \( \varepsilon = -M\,dI/dt \), not M itself.
Option (3) The materials of the wires of the coils — Incorrect. The metal of the wire changes the resistance of the coils, not the flux linkage.
Option (4) The current in the two coils — Incorrect. The flux linkage is proportional to the current, so their ratio M does not depend on the current.
NCERT (2026-27):
Mutual Inductance – “… 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.”