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A conducting circular loop of radius a and resistance R is kept in a horizontal plane. A vertical time varying magnetic field $B=2t$ is switched on at $t=0$ Then the flow of charge per unit time from any section of coil is

$(a)\;2 \pi R a^2 \\ (b)\;\large\frac{2 \pi a^2}{R} \\(c)\;\large\frac{\pi a^2}{R} \\(d)\;\large\frac{2 \pi}{a^2R} $

1 Answer

Flux $\phi =B.A$ as B is $\perp$ to the plane of coil.
$e= \large\frac{d \phi}{dt}$
$\quad= A \large\frac{dB}{dt}$
$\quad= \pi a^2 \large\frac{d}{dt}$$(2t)$
$\quad= 2\pi a^2$
The flow of charge is current $i= \large\frac{e}{R}$
$\qquad= \large\frac{2 \pi a^2}{R}$
Hence b is the correct answer.
answered Mar 21, 2014 by meena.p

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