JEE Main 2015 — Magnetic Effects of Current Question with Solution

For a magnetic dipole placed in a uniform magnetic field, the torque is given by $\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$, and potential energy $U$ is given as,

$U=-\overrightarrow{M}·\overrightarrow{B}=-MB\cos \theta$

When $\overrightarrow{M}$ is in the same direction as $\overrightarrow{B}$ then $\overrightarrow{\tau }=0$ and $U$ is minimum = $-MB$ as $\theta =0^o$.$\Rightarrow$ Stable equilibrium is (b).

When $\overrightarrow{M}$ the opposite direction of $\overrightarrow{B}$, then $\overrightarrow{\tau }=0$ and $U$ is max = $+MB$
As, $\theta ={180}^o$ $\Rightarrow$Unstable equilibrium in (d)