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Question

Two wires of same lengths are shaped into a square and a circle. If they carry same current, then the ratio of their magnetic moments is :

A
2:π
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B
π:2
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C
π:4
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D
4:π
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Solution

The correct option is C π:4
Magnetic moment of a loop is given by pm=IA
where, I= current through the loop
A= area of loop
Perimeter of square should be equal to the circumference of circle, since wires have same length.
Therefore, 4a=2πra=πr2 .....(i)
In figure (i), magnetic moment of square loop is given by
pm1=I(A1)
pm1=Iπ2r24 [from equation (i)] ....(ii)
In Fig. (ii), magnetic moment of circular loop is given by
pm2=I(A2)
pm2=I(πr2) ....(iii)
From equations (ii) and (iii), we get
pm1pm2=π4

707281_669991_ans_5b8693c03532405393064ae573f1a826.png

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