Question

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 :

• A. $\frac{n_{2}}{n_{1}}. \frac{r^{2}_{2}}{r_{1}^{2}}$
• B. $\frac{n_{2}}{n_{1}}. \frac{r_{1}}{r_{2}}$
• C. $\frac{n_1}{n_2}$
• D. $\frac{n_2}{n_1}$

Answer 1

Answer: (D)

$\frac{n_2}{n_1}$

Answer 2

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