A) \[\frac{l{{L}^{2}}}{4\pi }\]
B) \[\frac{lL}{4\pi }\]
C) \[\frac{{{l}^{2}}L}{4\pi }\]
D) \[\frac{{{l}^{2}}{{L}^{2}}}{4\pi }\]
Correct Answer: A
Solution :
Let a wire length L is bend in a circular form of radius r. \[2\pi r=L\,\,\,\,\,\Rightarrow \,\,\,\,\,r=\frac{L}{2\pi }\,\,\] The magnetic dipole moment of a circular ring \[\operatorname{M}=IA\] \[\operatorname{M}=l\pi {{r}^{2}}\] ... (ii) On putting the value of from Eq. (i), \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,M=l\pi {{\left( \frac{L}{2\pi } \right)}^{2}}=l\pi \frac{{{L}^{2}}}{4{{\pi }^{2}}}=\frac{l{{L}^{2}}}{4\pi }\]You need to login to perform this action.
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