Question

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

A
2:π
B
π:3
C
π:4
D
1:π

Solution

## The correct option is A $$\displaystyle \pi :4$$Let length of wire be $$l$$. For a square loop, side of square $$\displaystyle \frac { l }{ 4 }$$. Hence its magnetic moment$$\displaystyle { M }_{ sq } = iA=i{ \left[ \frac { l }{ 4 } \right] }^{ 2 }=\frac { i{ l }^{ 2 } }{ 16 }$$Radius of a circular loop $$\displaystyle r=\frac { l }{ 2\pi }$$.Hence, its magnetic moment$$\displaystyle { M }_{ cir }=iA=i\pi { r }^{ 2 }$$$$\displaystyle M_{cir}=i\pi \left[ \frac { { l }^{ 2 } }{ 4{ \pi }^{ 2 } } \right] =\frac { i{ l }^{ 2 } }{ 4\pi }$$$$\displaystyle \Rightarrow \quad \frac { { M }_{ sq } }{ { M }_{ cir } } =\frac { \pi }{ 4 }$$Physics

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