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  4. 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 rate of mutual inductance to the self-inductance of the inner-coil is :

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Q. 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 rate of mutual inductance to the self-inductance of the inner-coil is :

JEE MainJEE Main 2019Electromagnetic Induction

Solution:

$M = \mu_{0} n_{1}n_{2} \pi r^{2}_{1} $
$ L =\mu_{0} n_{1}^{2} \pi r^{2}_{1} $
$\Rightarrow \frac{M}{L} = \frac{n_{2}}{n_{1}} $