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A uniform circular loop of radius “a” and resistance “R” is placed perpendicular to a uniform magnetic field B. One half of the loop is rotated about the diameter with angular velocity $ω$ as shown. Then, the current in the loop is

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Zero, when $θ$ is zero

$\frac{π a^{2} B ω}{2 R},$ when $θ$ is zero

Zero, when $θ = \frac{π}{2}$

$\frac{π a^{2} B ω}{2 R},$ when $θ = \frac{π}{2}$

answer is A, D.

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Detailed Solution

$ϕ = \vec{B} . \vec{A} \Rightarrow ε = \frac{d ϕ}{d t}$
$ε = \frac{π R^{2} ω B \sin θ}{2}$
$θ = 0, i = 0$
$θ = \frac{π}{2}, i = \frac{B π a^{2} ω}{R}$

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