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

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Answer & Solution

Correct Answer

(A) \(\sqrt{2}\) \(abI\), along \(\left(\frac{\hat{j}}{\sqrt{2}}+\frac{\hat{ k }}{\sqrt{2}}\right)\)

Detailed explanation

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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