Question

A steel wire of length I has a magnetic moment M. It is then bent into a semicircular arc. The new magnetic moment is ______.

Options

• M × l

• `"M"/l`

• `"2M"/pi`

• M

Answer 1

A steel wire of length I has a magnetic moment M. It is then bent into a semicircular arc. The new magnetic moment is `underline("2M"/pi)`.

Explanation:

The length of wire, which is bent in form of semicircular arc of radius r is

l = πr

r = `l/pi`

The diameter of semicircular wire,

d = 2r = `("2"l)/pi`

∴ Magnetic moment of semicircular wire,

M' = `"m" xx "d" = "m" xx "2l"/pi`    ....(i)

The magnetic moment of straight wire,

M = ml

Substituting in Eq. (I), we get

M' = `"2M"/pi`