Question

A plane circular coil is rotated about its vertical diameter with a constant angular speed ω in a uniform horizontal magnetic field. Initially the plane of the coil is parallel to the magnetic field. Draw plots showing the variation of the following physical quantities as a function of ωt, where t represents time elapsed:

1. Magnetic flux Φ linked with the coil, and
2. emf induced in the coil.

Answer 1

Given: Plane of coil initially parallel to magnetic field. So, the angle between the area vector and the field = 90°.

Hence, Φ = 0 at t = 0.

Φ = `omega t + pi/2`

Magnetic flux through a rotating coil (Φ) = B A cos θ

= `B A cos(omega t + pi/2)`

= B A sin(ωt)

Magnetic flux varies sinusoidally with time, starting from zero. So, Φ vs ωt is a sine curve starting from the origin.

Induced emf (e) = `-(d phi)/dt`

= −BAω cos(ωt)

The graph shows a cosine curve, with a maximum at t = 0 and a phase difference of 90° with the flux.

b.