The mutual inductance of a pair of solenoids depends on

The correct answer is Option (1) → their separation as well as their relative orientation

The mutual inductance \( M \) is defined by \( \Phi_{2} = M I_{1} \): it is the flux linked with one coil per unit current in the other. It is a property of the pair of coils, fixed by their geometry (number of turns, size, separation, relative orientation) and by the medium or core between them.

Option (1) their separation as well as their relative orientation — Correct. The separation and the relative orientation decide how much of the flux of one solenoid links with the other.

Option (2) the material of the wires of the solenoid — Incorrect. The metal of the wire affects the resistance, not the flux linkage, so \( M \) does not depend on it.

Option (3) the currents in the two solenoids — Incorrect. \( M \) is the ratio of flux to current and does not change with the currents.

Option (4) rate of change of currents in the two solenoids — Incorrect. The rate of change of current decides the induced emf, \( \varepsilon = -M\,dI/dt \), but not \( M \) itself.

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.”