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(C) The net magnetic dipole moment of two magnets,each with dipole moment $M$,placed at an angle $	heta$ between them is given by the vector sum:$M_{

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$(c)$

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(C) The net magnetic dipole moment of two magnets,each with dipole moment $M$,placed at an angle $	heta$ between them is given by the vector sum:$M_{net} = \sqrt{M^2 + M^2 + 2M^2 \cos 	heta} = \sqrt{2M^2(1 + \cos 	heta)} = \sqrt{2M^2(2 \cos^2(	heta/2))} = 2M \cos(	heta/2)$.Analyzing the configurations:$(a)$ The magnets are at $	heta = 90^{\circ}$. $M_{net} = 2M \cos(45^{\circ}) = 2M(1/\sqrt{2}) = \sqrt{2}M \approx 1.414M$.$(b)$ The magnets are anti-parallel,$	heta = 180^{\circ}$. $M_{net} = 2M \cos(90^{\circ}) = 0$.$(c)$ The magnets are at $	heta = 30^{\circ}$. $M_{net} = 2M \cos(15^{\circ}) \approx 2M(0.966) = 1.932M$.$(d)$ The magnets are at $	heta = 60^{\circ}$. $M_{net} = 2M \cos(30^{\circ}) = 2M(\sqrt{3}/2) = \sqrt{3}M \approx 1.732M$.Comparing the values,the configuration in $(c)$ 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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