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JEE Main 2019 (11 Jan, Shift 1) · Mutual Inductance

Mutual Inductance question from JEE Main 2019 (11 Jan, Shift 1)

Q56JEE Main 2019 · 11 JAN · SHIFT 1Medium

Mutual Inductance

There are two long co-axial solenoids of same length $l$ . The inner and outer coils have radii r1 and r2 and number of turns per unit length n1 and n2, respectively. The ratio of mutual inductance to the self - inductance of the inner-coil is:

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Answer: (b)

Mutual inductance: field of outer coil $\mu_0 n_2 I$ links the inner coil, so $M = \mu_0 n_1 n_2 \pi r_1^2 l$ .
Self-inductance of inner coil: $L_1 = \mu_0 n_1^2 \pi r_1^2 l$
$\frac{M}{L_1} = \frac{n_2}{n_1}$
So the answer is (b) $\frac{n_2}{n_1}$ .

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