JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Electromagnetic Induction

Self-inductance of a coil, for instance a toroid, is $L=\frac{{\mu }_0{N}^{2}A}{2\pi R}$.

A: $L$ depends on the coil's geometry ($N$, $A$, $R$). True.

B: $L$ explicitly depends on the permeability of the medium (through ${\mu }_0$, or the core's $\mu$), so the claim that it does *not* depend on permeability is false.

C: By Lenz's law, the self-induced emf always opposes the change producing it. True.

D: Self-inductance plays the same role for current that mass plays for velocity — both resist a change in state — so it is the electromagnetic analogue of mass. True.

E: Establishing a current against the back-emf requires work, which is stored as magnetic energy $\frac{1}{2}L{I}^2$. True.

So A, C, D and E are correct, and B is false.