Regarding self-inductance:
A. The self-inductance of the coil depends on its geometry.
B. Self-inductance does not depend on the permeability of the medium.
C. Self-induced e.m.f. opposes any change in the current in a circuit.
D. Self-inductance is electromagnetic analogue of mass in mechanics.
E. Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

Solution

Physics sir · 4 steps

Look at L = μ₀ μᵣ n² A l for a solenoid: the medium sits right there, so B is the odd one out.

1. Check A and B. For a long solenoid, L = μ₀ μᵣ n² A l. It depends on the turns, area and length, which is the geometry, so A is true. It also depends on μᵣ, so filling the coil with iron raises L many times, and B is false.
2. Check C. The self-induced e.m.f. is ε = -L dI/dt. By Lenz's law it opposes any change in the current, whether the current is rising or falling, so C is true.
3. Check D and E. Inductance resists changes in current the way mass resists changes in velocity, and 1/2LI² matches 1/2mv², so D is true. To build up the current, the source must do work against the back e.m.f., and that work is stored as 1/2LI² in the magnetic field, so E is true.
4. So. A, C, D and E are correct and only B is wrong, which is option (c).

The idea to keep. Self-inductance depends on geometry and on the medium through μᵣ, never on the current itself. Think of it as electrical inertia: it opposes changes, and the work done against it is stored as 1/2LI².

Answer from the NTA final answer key. Solution by PrepWiser.