First slide

Faraday's law of Electromagnetic induction

Question

A metallic ring is rotating with uniform angular velocity about its diameter in a uniform magnetic field. Then emf induced in the ring is

Moderate

A

zero, when the plane of the coil is perpendicular to the field
B

maximum, when the plane of the coil is perpendicular to the field.
C

zero, when the plane of the coil is parallel to the field
D

maximum when the plane of the coil makes an angle of 45⁰ with the field.

Solution

At any time to,
$ϕ = \vec{A} . \vec{B} = ABcosθ = ABcosωt$
Induced emf, $ε = - \frac{dϕ}{dt} = AωB . sinωt = AωBsinθ$
Evidently, $ε$ is maximum when $θ = 90^{o}$ .
and $ε = 0$ when $θ = 0^{o}$ .
Here $\vec{A} =$ Area vector which is perpendicular to the plane of the coil.

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