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

The correct option is D $\frac{n_2}{n_1}$

$M={\mu }_0{n}_1{n}_2\pi r_1^2$
$L={\mu }_0{n}_1^2\pi r_1^2$
$\Rightarrow \frac{M}{L}=\frac{n_2}{n_1}$