JEE PYQ: Magnetic Effects Of Current Question 12
Question 12 - 2020 (02 Sep 2020 Shift 2)
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 $ABCDEFA$ is:
(1) $abI$, along $\left(\frac{\hat{j}}{\sqrt{2}} + \frac{\hat{k}}{\sqrt{2}}\right)$
(2) $\sqrt{2}abI$, along $\left(\frac{\hat{j}}{\sqrt{2}} + \frac{\hat{k}}{\sqrt{2}}\right)$
(3) $\sqrt{2}abI$, along $\left(\frac{\hat{j}}{\sqrt{5}} + \frac{2\hat{k}}{\sqrt{5}}\right)$
(4) $abI$, along $\left(\frac{\hat{j}}{\sqrt{5}} + \frac{2\hat{k}}{\sqrt{5}}\right)$
Show Answer
Answer: (1) $abI$, along $\left(\frac{\hat{j}}{\sqrt{2}} + \frac{\hat{k}}{\sqrt{2}}\right)$
Solution
$\vec{M}_1 = (abI)\hat{j}$, $\vec{M}_2 = (abI)\hat{k}$. Net $\vec{M} = abI(\hat{j} + \hat{k})$, direction along $\frac{\hat{j}}{\sqrt{2}} + \frac{\hat{k}}{\sqrt{2}}$.
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