A bar magnet of lenth `l` and magnetic dipole moment 'M' is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

Options

A. `3/pi M`
B. `2/pi M`
C. `M/2`
D. M.

Answer

a

Explanation

Initially, magnetic moment of the rod is given by `M = ml` (where l is the shortest distance between both the magnetic poles)
Now the rod is bent into a form of an are having a distance of r between both magnetic poles (as shown in the given figure).
Triangle ABC is an equilateral triangle, from the diagram, `l = pi/3 xx r rArr r = (3l)/pi`
Let m be the magnetic pole strength for the rod when the rod is bent, the new magnetic moment can be calculated as:
`M. = mr `
`M. = m ((3 xx l)/pi) `
`M. = 3/pi (ml)`
` M. = (3M)/pi `