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(B) The magnetic moment $\overrightarrow{M}$ of a current loop is given by $\overrightarrow{M} = I \overrightarrow{A}$,where the direction of area vec

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$(B)$ and $(D)$,respectively

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(B) The magnetic moment $\overrightarrow{M}$ of a current loop is given by $\overrightarrow{M} = I \overrightarrow{A}$,where the direction of area vector $\overrightarrow{A}$ is determined by the right-hand thumb rule.For stable equilibrium,the magnetic moment $\overrightarrow{M}$ must be parallel to the magnetic field $\overrightarrow{B}$ (i.e.,$	heta = 0^\circ$).For unstable equilibrium,the magnetic moment $\overrightarrow{M}$ must be anti-parallel to the magnetic field $\overrightarrow{B}$ (i.e.,$	heta = 180^\circ$).In figure $(a)$,the current flows in the $yz$-plane. By the right-hand rule,the area vector $\overrightarrow{A}$ points in the $+x$ direction.In figure $(b)$,the current flows in the $xy$-plane. By the right-hand rule,the area vector $\overrightarrow{A}$ points in the $+z$ direction. Since $\overrightarrow{B}$ is in the $+z$ direction,$\overrightarrow{M} \parallel \overrightarrow{B}$,which corresponds to stable equilibrium.In figure $(c)$,the current flows in the $xz$-plane. By the right-hand rule,the area vector $\overrightarrow{A}$ points in the $-y$ direction.In figure $(d)$,the current flows in the $xy$-plane. By the right-hand rule,the area vector $\overrightarrow{A}$ points in the $-z$ direction. Since $\overrightarrow{B}$ is in the $+z$ direction,$\overrightarrow{M}$ is anti-parallel to $\overrightarrow{B}$,which corresponds to unstable equilibrium.Therefore,$(b)$ is stable and $(d)$ is unstable.

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