Case: Read the passage and answer the question.
Consider two long co-axial solenoids, each of length l. We denote the radius of the inner solenoid S1 by \( r_1 \) and its number of turns per unit length by \( n_1 \). The corresponding quantities for the outer solenoid S2 are \( r_2 \) and \( n_2 \), respectively. Let \( N_1 \) and \( N_2 \) be the total numbers of turns of coils S1 and S2, respectively.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If the space inside the solenoids is filled with soft iron of relative permeability \( \mu_r \), their mutual inductance becomes \( \mu_r \) times its value in air.
Reason (R): The magnetic field inside a long solenoid does not depend on the material filling it.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) is correct but (R) is not correct.
Assertion (A) If the space inside the solenoids is filled with soft iron of relative permeability \( \mu_r \), their mutual inductance becomes \( \mu_r \) times its value in air. — True. With the iron present, the field of each solenoid is \( \mu_r \) times larger for the same current. So the flux linkage per unit current also grows \( \mu_r \) times, and \( M=\mu_r\mu_0n_1n_2\pi r_1^{2}l \).
Reason (R) The magnetic field inside a long solenoid does not depend on the material filling it. — False. The current fixes the magnetic intensity \( H \) inside the solenoid. The field is \( B=\mu_0\mu_rH \), so it does depend on the material inside.
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 μr had been present, the mutual inductance would be”
\( M=\mu_r\mu_0n_1n_2\pi r_1^{2}l \)
Magnetisation and Magnetic Intensity – “… we obtain,”
\( B=\mu_0(1+\chi)H \qquad (5.14) \)
\( =\mu_0\mu_rH \)\( =\mu H \qquad (5.15) \)