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…

There are two long co-axial solenoids of same length $\displaystyle l$. The inner and outer coils have radii $\displaystyle \mathrm{r}_1$ and $\displaystyle \mathrm{r}_2$ and number of turns per unit length $\displaystyle \mathrm{n}_1$ and $\displaystyle \mathrm{n}_2$, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is :