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.
How does the magnetic flux through a coil vary with the current that produces it?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Directly proportional to the current
A current in a coil sets up a magnetic field, and this field at every point is proportional to the current. The flux through the coil grows in the same way. For a coil of \( N \) turns linked with its own current, this is written as \( N\Phi_B=LI \), where \( L \) is the self-inductance of the coil.
Option (1) Inversely proportional to the current — Incorrect. A larger current makes a stronger field. It gives more flux through the coil, not less.
Option (2) Directly proportional to the current — Correct. Doubling the current doubles the field and so doubles the flux, \( \Phi_B\propto I \).
Option (3) Independent of the current — Incorrect. Here the flux is produced by the current itself. With no current there is no field and no flux.
Option (4) Proportional to the square of the current — Incorrect. By the Biot-Savart law the field of the coil varies as \( I \), not as \( I^{2} \). So the flux also varies as \( I \).
NCERT (2026-27):
Inductance – “… However, in both the cases, the flux through a coil is proportional to the current. That is, ΦB α I.”