Question

The effective radius of a circular coil is $R$ and number of turns is $N$. The current through it is $i$ ampere. The work done in rotating the coil by angle of $180^{\circ }$ in an external magnetic field $B$ will be (initially plane of coil is perpendicular to magnetic field)

• A. $\pi Ni{R}^{2}B$
• B. $2\pi Ni{R}^{2}B$
• C. $\frac{(2NiB)}{\pi R^2}$
• D. Zero

Answer 1

Answer: (B)

$W=\Delta U=U_f-U_i$
$=-Ni\pi R^2\cos 180^{\circ }-\left(-Ni\left(\pi R^2\right)\cos 0^{\circ }\right)$
$=2\pi Ni{R}^{2}B$