In an AC generator when the plane of the armature is perpendicular to the magnetic field, what will the magnitude of the magnetic flux passing through the coil and the emf induced in the coil be?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → The magnetic flux is maximum and the induced emf is zero
For a coil of N turns and area A rotating with angular speed \( \omega \) in a field B, with \( \theta = \omega t \) the angle between the normal to the coil and the field:
\( \displaystyle \Phi = NBA\cos\omega t \)
\( \displaystyle \varepsilon = -\frac{d\Phi}{dt} = NBA\omega\sin\omega t \)
When the plane of the coil is perpendicular to the field, its normal is along the field, so \( \theta = 0 \).
\( \cos 0 = 1 \;\Rightarrow\; \Phi = NBA \text{ (maximum)} \)
\( \sin 0 = 0 \;\Rightarrow\; \varepsilon = 0 \)
At this position the flux is at its peak and, for an instant, not changing; by Faraday's law the emf is the rate of change of flux, so the emf is zero.
Option (1) Both the magnetic flux and the induced emf are maximum — Incorrect. The flux is maximum, but its rate of change, and so the emf, is zero.
Option (2) Both the magnetic flux and the induced emf are zero — Incorrect. The flux and the emf are never zero together.
Option (3) The magnetic flux is zero and the induced emf is maximum — Incorrect. This happens when the plane of the coil is parallel to the field.
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).”
AC Generator – “… Note from Fig. 6.14 that the emf has its extremum value when θ = 90° or θ = 270°, as the change of flux is greatest at these points.”