A wire carrying current I is bent in the shape ABCDEFA


A wire carrying current $I$ is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA 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 $\mathrm{ABCDEFA}$ is :


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

  2. $\sqrt{2}$ abI, along $\left(\frac{\hat{\mathrm{j}}}{\sqrt{5}}+\frac{2 \hat{\mathrm{k}}}{\sqrt{5}}\right)$

  3. abI, along $\left(\frac{\hat{\mathrm{j}}}{\sqrt{2}}+\frac{\hat{\mathrm{k}}}{\sqrt{2}}\right)$

  4. abI, along $\left(\frac{\hat{\mathrm{j}}}{\sqrt{5}}+\frac{2 \hat{\mathrm{k}}}{\sqrt{5}}\right)$

Correct Option: 1




For $\mathrm{ABCD}$

$\overrightarrow{\mathrm{M}}_{1}=\mathrm{abI} \hat{\mathrm{K}}$


$\overrightarrow{\mathrm{M}}_{2}=\mathrm{abI} \hat{\mathrm{j}}$


$=a b I(\hat{k}+\hat{j})$

$=a b I \sqrt{2}\left(\frac{\hat{j}}{\sqrt{2}}+\frac{\hat{k}}{\sqrt{2}}\right)$


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