A magnetised steel wire of length L has a magnetic moment of `3.14 Am^(2)`. If the wire is bent into a semicircular arc, then what would be its new magnetic moment? (assume that the poles are situated at the ends of the wire.)

Options

A. `2M//pi`
B. `M//2pi`
C. `M//pi`
D. `M`

Answer

A

Explanation

Let pole strength of the wire is m then we can write the following:
`M = ml rArr m = m//l` ....(i)
Let R be the radius of the semicircle formed and for length l of the wire we can write the following:
`l = pi R rArr R = l//pi` .....(ii)
In case of semicircle distance between the two poles has become 2R and hence magnetic moment can be written as follows:
`M = m (2R) = (M//l) xx (2l // pi) = 2M // pi`