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  4. A circular ring of diameter 20 cm has a resistance of 0.01 Ω. The charge that will flow through the ring if it is turned from a position perpendicular to a uniform magnetic field of 2.0 T to a position parallel to the field is about

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Q. A circular ring of diameter $20\, cm$ has a resistance of $0.01 \,\Omega$. The charge that will flow through the ring if it is turned from a position perpendicular to a uniform magnetic field of $2.0\, T$ to a position parallel to the field is about

AIIMSAIIMS 2018Electromagnetic Induction

Solution:

As q $=\frac{-d\phi}{R}=\frac{BA\left(cos\,0^{\circ}-cos\,90^{\circ}\right)}{R}$
$=\frac{B\pi r^{2}\left(1+0\right)}{R}=\frac{B\pi r^{2}}{R}$
$=\frac{2\times3.14\times\left(10^{-1}\right)^{2}}{0.01}$
$=6.28\,C\,\simeq\,6.3\,C$