The magnetic moment of the arrangement shown | vedclass

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(C) The magnetic moment is a vector quantity. The direction of the magnetic moment is from the South pole $(S)$ to the North pole $(N)$.$1$. The horiz

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$2$

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(C) The magnetic moment is a vector quantity. The direction of the magnetic moment is from the South pole $(S)$ to the North pole $(N)$.$1$. The horizontal magnet has a magnetic moment $M$ directed towards the left.$2$. The vertical magnet has a magnetic moment $M$ directed upwards.$3$. The hypotenuse magnet has a magnetic moment $M\sqrt{2}$ directed along the hypotenuse (from $S$ to $N$).Let the horizontal direction be the $x$-axis and the vertical direction be the $y$-axis.- $\vec{M}_1 = -M \hat{i}$- $\vec{M}_2 = M \hat{j}$- $\vec{M}_3 = M\sqrt{2} (\cos 45^\circ \hat{i} + \sin 45^\circ \hat{j}) = M\sqrt{2} (\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j}) = M \hat{i} + M \hat{j}$Now,the resultant magnetic moment $\vec{M}_{	ext{net}}$ is:$\vec{M}_{	ext{net}} = \vec{M}_1 + \vec{M}_2 + \vec{M}_3 = (-M \hat{i} + M \hat{j}) + (M \hat{i} + M \hat{j}) = 2M \hat{j}$The magnitude of the resultant magnetic moment is $2M$. Therefore,the value is $2$.

The magnetic moment of the arrangement shown in the figure is ............. $M$.

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