A thin bar magnet of magnetic length L and original magnetic moment M is uniformly bent into a circular arc that subtends an angle φ at the centre, where φ is measured in radians.
Its new magnetic moment is:

Question

A thin bar magnet of magnetic length L and original magnetic moment M is uniformly bent into a circular arc that subtends an angle φ at the centre, where φ is measured in radians.

Its new magnetic moment is:

G1 Physics · Accepted Answer

Let pole strength be m and radius of the circular arc be R. Because φ is in radians, L = Rφ. The separation between the two poles is the chord: d = 2R sin(φ/2). Hence, M' = md. Also, M = mL. Therefore, M'/M = d/L = [2R sin(φ/2)]/(Rφ) = 2sin(φ/2)/φ. Thus, M' = M·2sin(φ/2)/φ.