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A thin circular wire carrying a current ...

A thin circular wire carrying a current I has a magnetic moment M. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment

A

M

B

`(4)/(pi^(2))""M`

C

`(4)/(pi)""M`

D

`(pi)/(4) "" M`

Text Solution

Verified by Experts

The correct Answer is:
D
`M_("square") = IA = I ((L)/(4))^(2) = (iL^2)/(16)`
`M_("circle") = I pi r^(2) = I pi ((L)/(2pi))^(2) = (iL^2)/(4pi)`
`M_("square") = (pi)/(4) M_("circle") ` or `(pi)/(4) M`
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