A magnetised wire of moment M is bent into an arc of a circle subtending an angle of 60^(@) at the centre. The new magnetic moment is

Options

A. `3M//pi`
B. `2M//pi`
C. `M//pi`
D. none of these

Answer

A

Explanation

Let L be the length of straight wire which is bent into an arc shown as AB in the figure. If R is the radius of circle then we can see in figure that direct distance between A and B is also equal to R, because OAB is equilateral triangle. If m is the pole strength of the equivalent bar magnet then new magnetic moment can be written as follows:
`M. = mR` ....(i)
Magnetic moment of straight wire can be written as follows:
M = mL
`m = M//L` ....(ii)
Length L represents 1/6 of the circumference of circle, hence we can write the following:
` L = (1//6) (2pi R) `
`rArr R = 3L // pi ` ...(iii)
Substituting values from equation (ii) and (iii) in equation (i) we get the following:
`M. = (M//L) (3L //pi) = 3M//pi`