Question

A magnet of magnetic moment $M$ is situated with its axis along the direction of a magnetic field of strength $B$. The work done in rotating it by an angle of ${180}^{\circ }$ will be

• A. $-MB$
• B. $+MB$
• C. $0$
• D. $+2MB$

Answer 1

The correct option is D $+2MB$

$W_{field}=-\Delta U=U_i-U_f$


$U\to$ Magnetic potential energy.

$\theta \to$ Angle between $\overrightarrow{M}$ and $\overrightarrow{B}$

$U=-\overrightarrow{M}\cdot \overrightarrow{B}$

Now, initially ${\theta }_i=0^{\circ }$

and finally ${\theta }_f={180}^{\circ }$

So,

$W_{field}=-MB\cos 0^{\circ }-(-MB\cos {180}^{\circ })$

$W_{field}=-MB-MB=-2MB$

Since, there is no change in kinetic energy of the system,

$\Rightarrow W_{ext}=-W_{field}=+2MB$

Hence, option $\left(D\right)$ is the correct answer.