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A circular loop and a square loop are fo...

A circular loop and a square loop are formed from the same wire and the same current is passed through them . Find the ratio of their dipole moments.

A

`4pi`

B

`(4)/(pi)`

C

`(2)/(pi)`

D

`2pi`

Text Solution

Verified by Experts

The correct Answer is:
B
Suppose the length of wire is l .
When , wire formed in circular loop then radius of loop ,
`r = (l)/(2pi) " " [because l = 2pi r]`
Magnet dipole , `M_(1) = iA`
`= ipi r^(2) = ipi xx ((l)/(2pi))^(2)`
= `ixx (l^(2))/(4pi)`
When wire formed in square loop then the side of loop ,
a = `(l)/(4)`
Magnet loop , `M_(2) = IA`
`=i xx a^(2)`
`= i xx (l^(2))/(16)`
`therefore " " (M_(1))/(M_(2)) = (4)/(pi)`
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Knowledge Check

  • When current is passed through a circular wire prepared from a conducting material, the magnetic field produced at its centre is B. Now a loop having two turns is prepared from the same wire and the same current is passed through it. The magnetic field at its centre will be :

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