A wire carrying current $I$ is bent in the shape $A\,B\,C\,D\,E\,F\,A$ as shown, where rectangle $A\,B\,C\,D\,A$ and $A\,D\,E\,F\,A$ are perpendicular to each other. If the sides of the rectangles are of lengths $a$ and $b,$ then the magnitude and direction of magnetic moment of the loop $A\,B\,C\,D\,E\,F\,A\,$ is
JEE MAIN 2020, Diffcult
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Sol. $\quad M=N I A$
$N =1$
For $ABCD$
$\overrightarrow{ M }_{1}= abI \hat{ K }$
For $DEFA$
$\overrightarrow{ M }_{2}= abI \hat{ j }$
$\overrightarrow{ M }=\overrightarrow{ M }_{1}+\overrightarrow{ M }_{2}$
$=\operatorname{ab} I (\hat{ k }+\hat{j})$
$=\operatorname{ab} I \sqrt{2}\left(\frac{\hat{j}}{\sqrt{2}}+\frac{\hat{ k }}{\sqrt{2}}\right)$
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