A bar magnet of length 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?

M=mL
Let the length of the bar magnet be l and magnetic dipole moment be M.
When the bar magnet is bent in the form of an arc, the length of the arc is l.
The radius of the arc is r = l/(2π/3) = 3l/(2π)
The magnetic dipole moment of a current loop is given by M = IA, where I is the current and A is the area of the loop.
In this case, the arc subtends an angle of 2π/3 radians at the center.
The area of the sector formed by the arc is A = (1/2)r²θ = (1/2)(3l/(2π))²(2π/3) = (3l²)/(4π)
The magnetic dipole moment of the arc is given by M' = m × A
The magnetic moment per unit length is m = M/l.
Therefore, the new magnetic dipole moment is M' = (M/l) × (3l²)/(4π) = (3M/4π)l.
The correct option is M/π.