The mutual inductance of a pair of solenoid depends :
(A) on their separation
(B) on their relative orientation
(C) on the current flowing
(D) on the number of turns in the solenoids
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (B) and (D) only
The mutual inductance \( M \) is the flux linked with one coil per unit current in the other, \( N_2\Phi_2 = M I_1 \). For two long coaxial solenoids, one inside the other,
\( \displaystyle M = \mu_0 n_1 n_2 \pi r_1^{2} l \)
So \( M \) depends only on the geometry of the pair (sizes, number of turns, how far apart and how they are oriented) and on the medium, not on the current.
(A) on their separation — Correct. Moving the coils apart reduces the flux of one that passes through the other, so \( M \) decreases with separation.
(B) on their relative orientation — Correct. If one coil is turned so that its axis is perpendicular to the other's, very little flux links the second coil, so orientation changes \( M \).
(C) on the current flowing — Incorrect. The flux linked is proportional to the current, so the ratio \( M = N_2\Phi_2/I_1 \) is independent of the current.
(D) on the number of turns in the solenoids — Correct. \( M \) is proportional to \( n_1 n_2 \), the turns per unit length of both solenoids.
NCERT (2026-27):
Mutual Inductance – “… Instead, if a medium of relative permeability μr had been present, the mutual inductance would be
\( \displaystyle M = \mu_r \mu_0 n_1 n_2 \pi r_1^2 l \)
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.”