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Q. A circular coil of radius $10 \,cm$ with $100$ turns carrying a current of $0.5$ A lies in a magnetic field of $2 T$ such that the normal drawn to the plane of the coil makes an angles $\theta$ with the direction of the field. Work done in rotating the coil to change the angle $\theta$ from $0^{\circ}$ to $180^{\circ}$ is

AP EAMCETAP EAMCET 2019

Solution:

Given, radius of coil, $R=10 \times 10^{-2}\, m$, number of turns in coil, $N=100$ turns, current through coil, $I=0.5 \,A$, magnetic field, $B=2 T$ and change in angle of rotating coil, $\theta=0^{\circ}$ to $180^{\circ}$.
Work done in turning a loop from angle $\theta_{1}$ to $\theta_{2}$.
$W=M B\left(\cos \theta_{1}-\cos \theta_{2}\right)$
$\Rightarrow \, W=NIA B\left[\cos 0^{\circ}-\cos 180^{\circ}\right]$
$\Rightarrow \,W=100 \times 0.5 \times \pi \times 100 \times 10^{-4} \times 2[1-(-1)]$
Hence, $W=2 \pi \,J$