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(C) The direction of the magnetic dipole moment is from the south pole to the north pole of the magnet.In configuration $(1)$,the angle between the tw

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$3$

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(C) The direction of the magnetic dipole moment is from the south pole to the north pole of the magnet.In configuration $(1)$,the angle between the two magnetic moments is $90^{\circ}$. The net magnetic dipole moment is $m_{	ext{net}} = \sqrt{m^2 + m^2 + 2m^2 \cos 90^{\circ}} = \sqrt{2m^2} = m\sqrt{2} \approx 1.414m$.In configuration $(2)$,the magnetic moments are in opposite directions,so the angle is $180^{\circ}$. The net magnetic dipole moment is $m_{	ext{net}} = m - m = 0$.In configuration $(3)$,the angle between the two magnetic moments is $30^{\circ}$. The net magnetic dipole moment is $m_{	ext{net}} = \sqrt{m^2 + m^2 + 2m^2 \cos 30^{\circ}} = \sqrt{2m^2 + 2m^2(\frac{\sqrt{3}}{2})} = m\sqrt{2 + \sqrt{3}} \approx m\sqrt{3.732} \approx 1.932m$.In configuration $(4)$,the angle between the two magnetic moments is $60^{\circ}$. The net magnetic dipole moment is $m_{	ext{net}} = \sqrt{m^2 + m^2 + 2m^2 \cos 60^{\circ}} = \sqrt{2m^2 + 2m^2(\frac{1}{2})} = m\sqrt{3} \approx 1.732m$.Comparing the values,configuration $(3)$ has the highest net magnetic dipole moment.

The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole moment $\vec{m}$. Which configuration has the highest net magnetic dipole moment?

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