Question

A circular coil of 100 turns and effective diameter 20 cm carries a current of 0.5 A. It is to be turned in a magnetic field of $B=2.0T$ from a position in which the normal to the plane of the coil makes an angle $\theta$ equals to zero to one in which $\theta$ equals to ${180}^o$. The work required in this process is:

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

Answer 1

The correct option is B $2\pi J$

Work done is change in potential energy.

Potential energy is given by $U=-\overrightarrow{M}.\overrightarrow{B}$

Work done,
$W=MB\cos {\theta }_1-MB\cos {\theta }_2$ (M is magnetic moment)
$=0.5\times \pi \times (0.1{)}^2\times 100\times 2cos0-0.5\times \pi \times (0.1{)}^2\times 100\times 2\times cos\pi$
$=\pi +\pi$
$=2\pi J$