Question

There are two long co-axial solenoids of same length $l$. The inner and outer coils have radii $r_1\text{and}{r}_2$ and number of turns per unit length $n_1\text{and}{n}_2$, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:

• A. $\frac{n_1}{n_2}$
• B. $\frac{n_2}{n_1}.\frac{r_1}{r_2}$
• C. $\frac{n_2}{n_1}.\frac{r_2^2}{r_1^2}$
• D. $\frac{n_2}{n_1}$

Answer 1

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

The mutual inductance of the co-axial solenoid is given by,

$M={\mu }_0{n}_1{n}_2\pi r_1^{2}l---\left(1\right)$

The self inductance of the inner solenoid is given by,

$L={\mu }_0{n}_1^2\pi r_1^{2}l---\left(2\right)$

$\Rightarrow \frac{M}{L}=\frac{n_2}{n_1}$

Hence, option $\left(D\right)$ is correct.