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. `5 Am^(2)`
B. `4 Am^(2)`
C. `3 Am^(2)`
D. `2 Am^(2)`

Answer

D

Explanation

Magnetic pole strength `m=M/L`
When the wire is bent into a semicircular arc, its two poles will be at a distance of 2r.
`:' L=pir :. r=L/pi`
`:.` New magnetic length `2r=(2L)/pi`
`:.` New magnetic moment
= pole strength `xx` magnetic length
`M'=M/Lxx(2L)/pi=(2M)/pi`
`:. M'=(2xx3.14)/3.14 =2 Am^(2)`