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

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Aicharya · Accepted Answer

Three magnetic moments of magnetic dipole, are shown in the figure below as,

Here, $M_1=\sqrt{M_A^2+M_B^2+2 M_A M_B \cos 90^{\circ}}$ $\begin{aligned} & \Rightarrow \quad M_1=\sqrt{M^2+M^2+0} \\ & \Rightarrow \quad M_1=M \sqrt{2} \end{aligned}$ Now, the resultant, magnetic moment, $\begin{aligned} & M_{\text {resultant }}=M_1+M_C \\ & \left(\because M_1 \text { and } M_C\right. \text { are } \\ \Rightarrow \quad & M_{\text {resultant }}=M \sqrt{2}+M \\ \Rightarrow \quad & M_{\text {resultant }}=(1+\sqrt{2}) \mathrm{M} \end{aligned}$ $(\because M_1 \text { and } M_C \text { are in the same direction) }$ $\therefore$ correct option is (b).

The resultant magnetic moment of three magnetic dipoles, each of the magnetic moment \(M\) shown in the…

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