Case: Read the passage and answer the question.
The number of magnetic field lines crossing a surface is called the magnetic flux. An electric current can be induced in a coil by a flux change produced by another coil in its vicinity or by a flux change produced by the same coil. The former is called mutual induction and the latter is called self-induction. An induction furnace works on this principle.
The inductance of a coil depends only on
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → the geometry of the coil and the intrinsic material properties
The inductance of a coil is the constant of proportionality in \( N\Phi_B=LI \), the flux linkage per unit current.
Option (1) the geometry of the coil and the intrinsic material properties — Correct. For a long solenoid with a core, \( L=\mu_r\mu_0n^2Al \). The turns, area and length are the geometry of the coil. The relative permeability \( \mu_r \) of the core is an intrinsic material property. Nothing else enters \( L \).
Option (2) the current through the coil — Incorrect. The flux linkage \( N\Phi_B \) is proportional to the current, so doubling \( I \) doubles \( N\Phi_B \) and their ratio \( L \) stays the same.
Option (3) the rate of change of current in the coil — Incorrect. The rate \( dI/dt \) decides the size of the self-induced emf \( \varepsilon=-L\,dI/dt \). \( L \) itself is a property of the coil.
Option (4) the emf induced in the coil — Incorrect. The induced emf \( \varepsilon=-L\,dI/dt \) is a result of the changing current. It changes with \( dI/dt \), but \( L \) stays the same.
NCERT (2026-27):
Inductance – “The constant of proportionality, in this relation, is called inductance. We shall see that inductance depends only on the geometry of the coil and intrinsic material properties.”