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A circular coil of n turns and radius r is placed in a uniform magnetic field B. Initially the plane of the coil is perpendicular to the field. The coil is rotated through 90°. Its resistance is R. the quantity of charge passing through the coil is

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$π n^{2} rB / R$

$2 π n r^{2} VB / R$

$π n r^{2} B / R$

answer is D.

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Detailed Solution

Area of coil, $(A) = π r^{2}$

Magnetic flux of coil $= NBAcos 0^{\circ} = NBA .$

$ϕ = NBA$

$∴$ induced emf is $|e| = \frac{d ϕ}{d t}$

As we know,

induce current is, $i = \frac{|e|}{R} = \frac{d ϕ}{d} \frac{1}{R}$

$\begin{aligned} \Rightarrow i R = \frac{d ϕ}{d t} \\ \frac{d q}{d t} R = \frac{d ϕ}{d t} \end{aligned}$

$Q = \frac{ϕ}{R}$

$\frac{N B A}{R} = \frac{N B \times π r^{2}}{R}$

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