When the coil (armature) of an ac generator is set into rotation, what happens to the magnetic flux through the coil?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → It both increases and decreases.
When the coil turns with a constant angular speed \( \omega \), the angle between the field \( \vec{B} \) and the area vector \( \vec{A} \) is \( \theta=\omega t \). So the magnetic flux through the coil is \( \Phi_B=BA\cos\omega t \). It swings between \( +BA \) and \( -BA \) in every rotation.
Option (1) It increases. — Incorrect. The flux grows only during part of each turn. As the coil turns on, \( \cos\omega t \) falls again, so the flux cannot keep increasing.
Option (2) It decreases. — Incorrect. The flux falls only during part of each turn and then rises again, so it cannot keep decreasing.
Option (3) It both increases and decreases. — Correct. The effective area \( A\cos\omega t \) facing the field changes as the coil turns, so the flux \( BA\cos\omega t \) rises and falls periodically. This changing flux induces the alternating emf.
Option (4) It remains unaffected. — Incorrect. \( B \) and \( A \) stay the same, but the angle between them changes with time. A constant flux would induce no emf at all.
NCERT (2026-27):
AC Generator – “When the coil is rotated with a constant angular speed ω, the angle θ between the magnetic field vector B and the area vector A of the coil at any instant t is θ = ωt (assuming θ = 0° at t = 0). As a result, the effective area of the coil exposed to the magnetic field lines changes with time, … the flux at any time t is
\( \Phi_B=BA\cos\theta=BA\cos\omega t \)”