Which of the following loops is in stable equ | vedclass

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(D) For a current-carrying loop to be in stable equilibrium in an external magnetic field $\overrightarrow{B}$,its potential energy $U$ must be minimu

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(D) For a current-carrying loop to be in stable equilibrium in an external magnetic field $\overrightarrow{B}$,its potential energy $U$ must be minimum.The potential energy is given by $U = -\overrightarrow{M} \cdot \overrightarrow{B} = -MB \cos 	heta$,where $\overrightarrow{M}$ is the magnetic moment of the loop and $	heta$ is the angle between $\overrightarrow{M}$ and $\overrightarrow{B}$.$U$ is minimum when $\cos 	heta = 1$,which implies $	heta = 0^{\circ}$. This means the magnetic moment $\overrightarrow{M}$ must be parallel to the magnetic field $\overrightarrow{B}$.Using the right-hand rule to find the direction of $\overrightarrow{M}$ for each loop:- In option $A$,the current flows in the $yz$-plane. By the right-hand rule,$\overrightarrow{M}$ points along the $+x$-axis. Since $\overrightarrow{B}$ is along the $+y$-axis,$	heta = 90^{\circ}$.- In option $B$,the current flows in the $xy$-plane. By the right-hand rule,$\overrightarrow{M}$ points along the $+z$-axis. Since $\overrightarrow{B}$ is along the $+y$-axis,$	heta = 90^{\circ}$.- In option $C$,the current flows in the $xy$-plane. By the right-hand rule,$\overrightarrow{M}$ points along the $-z$-axis. Since $\overrightarrow{B}$ is along the $-z$-axis,$	heta = 0^{\circ}$.- In option $D$,the current flows in the $yz$-plane. By the right-hand rule,$\overrightarrow{M}$ points along the $+x$-axis. Since $\overrightarrow{B}$ is along the $+x$-axis,$	heta = 0^{\circ}$.Both $C$ and $D$ represent stable equilibrium. Based on standard representations,$D$ is the most common example.

Which of the following loops is in stable equilibrium?

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