A current carrying loop is placed in a uniform magnetic field in...

As we know that, potential energy of a magnet in a magnetic field $$\begin{aligned} U & =-\mathbf{m} \cdot \mathbf{B} \\ & =-m B \cos \theta\end{aligned}$$ where, $m=$ magnetic dipole moment of the magnet $B=$ magnetic field Case I $\theta=180^{\circ}$ $\therefore \quad U_1=-m B \cdot \cos 180^{\circ}$ $=m B \quad\left[\because \cos 180^{\circ}=-1\right]$ Case II $\theta=90^{\circ}$ $U_2=0 \quad\left[\because \cos 90^{\circ}=0\right]$ Case III $\theta$ is acute angle $$\begin{aligned} & & \in\left(0,90^{\circ}\right) \\ \therefore & \cos \theta & =\text{ positive } \\ \text{ Thus, } & U_3 & =\text{ negative }\end{aligned}$$ Case IV $\theta$ is obtuse $$\begin{array}{rlrl} & & \theta \in\left(90^{\circ}, 180^{\circ}\right) \\ \therefore \quad & \cos \in(0,-1)\end{array}$$ Thus, $\quad U_4=$ positive Therefore, decreasing order of $P E$ is I $\gt$ IV $\gt$ II $\gt$ III