Magnetic Effects Of Current Question 445

Question: A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the Loop will be:

Options:

A) $ \frac{2{\mu_{0}}Ii}{3\pi } $

B) $ \frac{{\mu_{0}}Ii}{2\pi } $

C) $ \frac{2{\mu_{0}}IiL}{3\pi } $

D) $ \frac{{\mu_{0}}IiL}{2\pi } $

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Answer:

Correct Answer: A

Solution:

[a] The net force on the loop $ F_{net}=F_{AB}+F_{BC}+F_{CD}+F_{AD} $
$ \Rightarrow ,F_{net}=\frac{{\mu_{0}}iI}{\pi }-\frac{{\mu_{0}}iI}{3\pi }=\frac{2{\mu_{0}}iI}{3\pi } $