JEE Main 2025 Jan 23 Shift 1, Physics Q1: Inductance

The self-inductance of any coil takes the form $L\propto \mu N^2\cdot (\text{geometric factor})$. For example, for a solenoid $L={\mu }_0{\mu }_r{n}^{2}V$, and for a circular loop $L\propto \frac{{\mu }_0{N}^{2}A}{2\pi R}$.

So $L$ depends on geometry (A ✓), depends on the permeability of the medium (B ✗), the induced emf opposes the change in current via Lenz's law (C ✓), $L$ plays the role of 'inertia' for current and stores energy as $\frac{1}{2}L{I}^2$ much like kinetic energy $\frac{1}{2}m{v}^2$ (D ✓), and work must be done against the back-emf to set up the current (E ✓).

Hence the correct set is A, C, D, E only.