Q 12-06-003NEETNEET 2026Top questionEasy
Consider a long solenoid of length $l$ and radius $r$. If $n$ is the number of turns per unit length and $\mu_0$ is the permeability of free space, the inductance of the solenoid is :
Answer: (A) $\mu_0 \pi n^2 r^2 l$
Field inside the solenoid: $B = \mu_0 n I$. Total turns $N = nl$, cross-section area $A = \pi r^2$.
Flux linkage:
$$N\phi = (nl)(\mu_0 n I)(\pi r^2) = \mu_0 \pi n^2 r^2 l\, I$$
So
$$L = \frac{N\phi}{I} = \mu_0 \pi n^2 r^2 l$$
Solution by Sreeraj P, M.Sc Physics