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.
For a coil whose shape does not change, the flux linkage \( N\Phi_B \) is proportional to the current \( I \) in it. The emf induced in the coil by a change in its own current is proportional to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( dI/dt \)
By Faraday’s law, the induced emf depends on how fast the flux linkage changes, \( |\varepsilon|=d(N\Phi_B)/dt \). The coil keeps its shape, so \( N\Phi_B \) is a fixed constant \( L \) times \( I \).
Option (1) the current \( I \) — Incorrect. A large steady current gives a large flux. But a steady flux induces no emf at all.
Option (2) \( I^{2} \) — Incorrect. The flux linkage grows in direct proportion to \( I \). So the square of the current does not enter the emf.
Option (3) \( I\,dI/dt \) — Incorrect. This product gives the rate at which energy is stored in the coil, \( d(\frac{1}{2}LI^{2})/dt=LI\,dI/dt \). The emf itself is \( L\,dI/dt \), with no extra factor \( I \).
Option (4) \( dI/dt \) — Correct. Since \( N\Phi_B\propto I \), the rate of change \( d(N\Phi_B)/dt \) is proportional to \( dI/dt \). So the emf is proportional to \( dI/dt \).
NCERT (2026-27):
Inductance – “… However, in both the cases, the flux through a coil is proportional to the current. That is, ΦB ∝ I.”
Inductance – “Further, if the geometry of the coil does not vary with time then,”
\( \displaystyle \frac{d\Phi_B}{dt}\propto\frac{dI}{dt} \)