Question

Two solenoids of equal number of turns having their length and the radii in the same ratio $1 : 2$. The ratio of their self-inductance will be

• A. 1:02
• B. 2:01
• C. 1:01
• D. 1:04

Answer 1

The Correct Option is A

For solenoids, self inductance is given by,
$L=\frac{\mu_{0} N^{2} A}{l}$
$\therefore \frac{L_{1}}{L_{2}}=\frac{\left(\frac{\pi r_{1}^{2}}{l_{1}}\right)}{\left(\frac{\pi r_{2}^{2}}{I_{2}}\right)}=\frac{\left(\frac{r_{1}^{2}}{l_{1}}\right)}{\left(\frac{r_{2}^{2}}{l_{1}}\right)}$
or $\frac{L_{1}}{L_{2}}=\frac{1}{2}$
$\left(\because \frac{r_{1}^{2}}{l_{1}} / \frac{r_{2}^{2}}{l_{2}}=1 / 2\right)$