There are two long co-axial solenoids of same length l. The inner and outer coils have radii r_1 and r_2 and number of turns per unit length n_1 and n_2, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:

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Correct answer: D. n_2 n_1

The rate of mutual inductance is given by M = _0 n _1 n _2 ~m _1^2 ....(i) The rate of self inductance is given by L = _0 n _1^2 r _1^2 .....(ii) Dividing (i) by (ii) M L = n _2 n _1

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