Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is
Diffcult
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(c) Suppose length of each wire is $l$. ${A_{square}} = {\left( {\frac{l}{4}} \right)^2} = \frac{{{l^2}}}{{16}}$
${A_{cirle}} = \pi {r^2} = \pi {\left( {\frac{l}{{2\pi }}} \right)^2} = \frac{{{l^2}}}{{4\pi }}$
Magnetic moment
$M = iA$
$ \Rightarrow \frac{{{M_{square}}}}{{{M_{cirde}}}} = \frac{{{A_{square}}}}{{{A_{cirde}}}}$
$ = \frac{{{l^2}/16}}{{{l^2}/4\pi }}$$ = \frac{\pi }{4}$
${A_{cirle}} = \pi {r^2} = \pi {\left( {\frac{l}{{2\pi }}} \right)^2} = \frac{{{l^2}}}{{4\pi }}$
Magnetic moment
$M = iA$
$ \Rightarrow \frac{{{M_{square}}}}{{{M_{cirde}}}} = \frac{{{A_{square}}}}{{{A_{cirde}}}}$
$ = \frac{{{l^2}/16}}{{{l^2}/4\pi }}$$ = \frac{\pi }{4}$
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