Question

A wire of fixed length is wound on a solenoid of length $‘{\ell }^{\prime }$ and radius ‘r’. Its self inductance is found to be L. Now if same wire is wound on a solenoid of length $\frac{\ell }{2}$ and $\frac{r}{2}$, then the self inductance will be:

• A. 2L
• B. L
• C. 4L
• D. 8L

Answer 1

The correct option is A

2L

$L=\frac{{\mu }_0{N}^2\pi r^2}{1}$ Length of wire $=N2\pi r=$ Constant (= C Suppose) Hence $L\alpha \frac{1}{\ell }\therefore$ Self inductance will become 2L.