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. $\pi N i R^{2} B$
• B. $2 \pi NiR ^{2} B$
• C. $\frac{(2 N i B)}{\pi R^{2}}$
• D. Zero

Answer 1

Answer: (B)

$ W =\Delta U=U_{f}-U_{i}$
$=-N i \pi R^{2} \cos 180^{\circ}-\left(-N i\left(\pi R^{2}\right) \cos 0^{\circ}\right) $
$=2 \pi N i R^{2} B$