A) \[2:\pi \]
B) \[\pi :2\]
C) \[\pi :4\]
D) \[4:\pi \]
Correct Answer: C
Solution :
(c) \[\pi :4\] According to question, Perimeter of square should be equal to circumference of circle \[\therefore 4a=2\pi r\Rightarrow a=\pi r/2\] ...(1) Magnetic moment of square wire. \[{{M}_{1}}=l({{A}_{1}})=\frac{l{{\pi }^{2}}{{r}^{2}}}{4}\] (from eq.(1))...(2) Magnetic moment of circular wire. \[{{M}_{2}}=l({{A}_{2}})=l\pi {{r}^{2}}\] ...(3) Required ratio, \[\frac{{{\mu }_{1}}}{{{\mu }_{2}}}=\frac{l{{\pi }^{2}}{{r}^{2}}}{4}\times \frac{1}{l\pi {{r}^{2}}}=\frac{\pi }{4}\]
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