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) $\mu_0 \pi n^2 r^2 l$
Concept. $L = \dfrac{N\phi}{I}$, with $B = \mu_0nI$ inside a long solenoid.
Step 1. Flux linkage. $N = nl$, $A = \pi r^2$:
$$N\phi = (nl)(\mu_0nI)(\pi r^2) = \mu_0\pi n^2r^2l\,I$$
Step 2. Inductance. $L = \mu_0\pi n^2r^2l$.
Answer. $\mu_0\pi n^2r^2l$ (Option A).
Solution by Sreeraj P, M.Sc Physics