A rectangular metallc loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf () with time (t) is given by [2025

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Solution

Q.
A coil of area A and N turns is rotating with angular velocity $ω$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $\vec{B}$ . Magnetic flux $φ$ and induced emf $ε$ across it, at an instant when $\vec{B}$ is parallel to the plane of coil, are: [2025]

1 $φ = A B, ε = 0$

2 $φ = 0, ε = N A B ω$

3 $φ = 0, ε = 0$

4 $φ = A B, ε = N A B ω$

Ans.
(2)

$ϕ = N B A \cos θ$

$ε = - \frac{d ϕ}{d t} = - N B A \frac{d (\cos θ)}{d t}$

$θ = ω t$

$ε = - N B A ω \sin ω t$

if B is parallel to plane of coil

$ω = 90 °$

$ϕ = 0, E = B A ω N$

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