Q. 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 :
A) $2\mu_0\pi n^2r^2l$
B) $\mu_0\pi n^2r^2l$
C) $\mu_0 n^2r^2l$
D) $\frac{\mu_0}{2\pi}n^2r^2l$
Explanation
[Solution from source] Inside the solenoid $B=\mu_0 nI$; flux linkage $=(nl)(\mu_0 nI)(\pi r^2)$, so $L=\mu_0 n^2\pi r^2 l$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.