The resultant magnetic moment of three magnet | vedclass

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(B) Let the three magnetic moments be $M_A$,$M_B$,and $M_C$,where $M_A = M_B = M_C = M$.First,we find the resultant of $M_A$ and $M_B$,which are at an

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$(\sqrt{2}+1) M$

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(B) Let the three magnetic moments be $M_A$,$M_B$,and $M_C$,where $M_A = M_B = M_C = M$.First,we find the resultant of $M_A$ and $M_B$,which are at an angle of $90^{\circ}$ to each other.The resultant $M_1$ is given by:$M_1 = \sqrt{M_A^2 + M_B^2 + 2 M_A M_B \cos 90^{\circ}}$$M_1 = \sqrt{M^2 + M^2 + 0} = M \sqrt{2}$The direction of $M_1$ is along the angle bisector of $M_A$ and $M_B$,which is in the same direction as $M_C$.Now,the total resultant magnetic moment $M_{	ext{resultant}}$ is:$M_{	ext{resultant}} = M_1 + M_C$$M_{	ext{resultant}} = M \sqrt{2} + M = (\sqrt{2} + 1) M$Therefore,the correct option is $(b)$.

The resultant magnetic moment of three magnetic dipoles,each of magnetic moment $M$,shown in the arrangement is:

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