Question

Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is

• A. 635056391475347954_8393962.PNG
• B. 635056391718625891_9163182.PNG
• C. 635056391868154270_7594690.PNG
• D. 635056392024713874_8411160.PNG

Answer 1

The correct option is C 635056391868154270_7594690.PNG

Suppose length of each wire is l.
$A_{square}={\left(\frac{l}{4}\right)}^2=\frac{l^2}{16}$
$A_{circle}=\pi r^2=\pi {\left(\frac{l}{2\pi }\right)}^2=\frac{l^2}{4\pi }$
$\because$ Magnetic moment
M=iA
$\Rightarrow \frac{M_{square}}{M_{circle}}=\frac{A_{square}}{A_{circle}}$
$\frac{l^2/16}{l^2/4\pi }=\frac{\pi }{4}$