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(C) magnetic dipole is in equilibrium in an external magnetic field when its magnetic moment $\vec{m}$ is parallel or anti-parallel to the magnetic fi

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$PQ_1, PQ_2$

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(C) magnetic dipole is in equilibrium in an external magnetic field when its magnetic moment $\vec{m}$ is parallel or anti-parallel to the magnetic field $\vec{B}$ (i.e.,$	heta = 0^{\circ}$ or $180^{\circ}$).At point $O$,the magnetic needle $P$ has a magnetic moment pointing upwards.For any magnet $Q$ placed at a position,it experiences a magnetic field $\vec{B}$ due to the dipole $P$. The system is in equilibrium if the magnetic moment $\vec{m}_Q$ of magnet $Q$ is parallel or anti-parallel to the magnetic field $\vec{B}$ produced by $P$ at that location.$1$. At $Q_1$ and $Q_2$ (axial positions),the magnetic field $\vec{B}$ is parallel to the magnetic moment of $P$. However,the orientation of $Q_1$ and $Q_2$ is horizontal,while the field is vertical. Thus,they are not in equilibrium.$2$. At $Q_3, Q_4, Q_5, Q_6$ (equatorial positions),the magnetic field $\vec{B}$ is anti-parallel to the magnetic moment of $P$. The orientation of these magnets is vertical,which is parallel/anti-parallel to the field,so they are in equilibrium.Therefore,the system is not in equilibrium for configurations $PQ_1$ and $PQ_2$.

$A$ small magnetized needle $P$ is placed at point $O$,and the arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations) of another identical magnet $Q$. In which configuration is the system $NOT$ in equilibrium?

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