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 :- [NEET - 2016] |
A) \[\frac{2{{\mu }_{0}}li}{3\pi }\]
B) \[\frac{{{\mu }_{0}}li}{2\pi }\]
C) \[\frac{2{{\mu }_{0}}liL}{3\pi }\]
D) \[\frac{{{\mu }_{0}}liL}{2\pi }\]
Correct Answer: A
Solution :
[a] |
\[{{F}_{AB}}=i\ell B\,\,(Attractive)\] |
\[{{F}_{AB}}=i(L).\frac{{{\mu }_{0}}I}{2\pi \left( \frac{L}{2} \right)}(\leftarrow )=\frac{{{\mu }_{0}}il}{\pi }(\leftarrow )\] |
\[{{F}_{(BC)}}(\uparrow )\] and \[{{F}_{(AD)}}(\uparrow )\] |
\[\Rightarrow \] cancel each other |
\[{{F}_{CD}}=i\ell B\,\,(Repulsive)\] |
\[{{F}_{CD}}=i(L)\frac{{{\mu }_{0}}I}{2\pi \left( \frac{3L}{2} \right)}(\to )=\frac{{{\mu }_{0}}iI}{3\pi }(\to )\] |
\[\Rightarrow \] \[{{F}_{net}}=\frac{{{\mu }_{0}}iI}{\pi }-\frac{{{\mu }_{0}}iI}{3\pi }=\frac{2{{\mu }_{0}}iI}{3\pi }\] |
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