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 $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:
Correct Option: , 4
(4) The rate of mutual inductance is given by
$\mathrm{M}=\mu_{0} \mathrm{n}_{1} \mathrm{n}_{2} \pi \mathrm{r}_{1}^{2}$ ...(1)
The rate of self inductance is given by
$\mathrm{L}=\mu_{0} \mathrm{n}_{1}^{2} \pi \mathrm{r}_{1}^{2} \ldots$ (ii)
Dividing (i) by (ii)
$\Rightarrow \frac{\mathrm{M}}{\mathrm{L}}=\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}$
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