A) \[\frac{\sqrt{2}i{{L}^{2}}}{8\pi }\]
B) \[\sqrt{3}\frac{i{{L}^{2}}}{4\pi }\]
C) \[\frac{i{{L}^{2}}}{4\pi }\]
D) \[\frac{i{{L}^{2}}}{2\pi }\]
Correct Answer: A
Solution :
Magnetic moment of circular loop: \[M=iA=i(\pi {{R}^{2}}).\] where \[L=2\pi R\] \[=\frac{i{{L}^{2}}}{4\pi }\] ?..(i) Magnetic moment of each semicircle \[M'=\frac{iA}{2}=\frac{i{{L}^{2}}}{8\pi }\] ........(ii) [From (i)] Magnetic moment of system :- \[{{M}_{net}}=\sqrt{{{M}^{'2}}+{{M}^{'2}}}\] \[=\sqrt{2}M'=\sqrt{2}\frac{i{{L}^{2}}}{8\pi }\] [From(ii)]You need to login to perform this action.
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