Q 12-06-137JEE MainJEE Main 2019 (11 Jan, Shift 1)Easy
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:
Answer: (D) $\dfrac{n_2}{n_1}$
The field of the outer coil, $\mu_0n_2i$, threads the inner coil's area $\pi r_1^2$:
$$M = \mu_0n_1n_2\pi r_1^2l,\qquad L_1 = \mu_0n_1^2\pi r_1^2l$$
$$\frac{M}{L_1} = \frac{n_2}{n_1}$$
Solution by Sreeraj P, M.Sc Physics