Question

A circular coil of radius $10cm$ with $100$ turns carrying a current of $0.5$ A lies in a magnetic field of $2T$ 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

• A. $\pi J$
• B. $2\pi J$
• C. $4\pi J$
• D. $8\pi J$

Answer 1

Answer: (B)

Given, radius of coil, $R=10\times 10^{-2}m$, number of turns in coil, $N=100$ turns, current through coil, $I=0.5A$, magnetic field, $B=2T$ and change in angle of rotating coil, $\theta =0^{\circ }$ to $180^{\circ }$.
Work done in turning a loop from angle ${\theta }_1$ to ${\theta }_2$.
$W=MB\left(\cos {\theta }_1-\cos {\theta }_2\right)$
$\Rightarrow W=NIAB\left[\cos 0^{\circ }-\cos 180^{\circ }\right]$
$\Rightarrow W=100\times 0.5\times \pi \times 100\times 10^{-4}\times 2[1-(-1)]$
Hence, $W=2\pi J$