A bar magnet of magnetic length 2l and pole strength m is bent at its centre so that its two equal halves make an angle 60° with each other. Pole strength remains unchanged. If its initial magnetic moment was M₀, the magnitude of the new magnetic moment is:
Options

Question

A bar magnet of magnetic length 2l and pole strength m is bent at its centre so that its two equal halves make an angle 60° with each other. Pole strength remains unchanged. If its initial magnetic moment was M₀, the magnitude of the new magnetic moment is:

Options

G1 Physics · Accepted Answer

Initially, M₀ = m(2l). After bending, the magnetic moment is m times the straight-line separation between the two poles. Each half has length l and the angle between the two halves is 60°. The pole separation is the resultant of two vectors of magnitude l with included angle 60°: d = √(l²+l²+2l²cos60°) = √(3l²) = √3 l. Hence, M = md = √3 ml. Since M₀ = 2ml, M/M₀ = √3/2. Therefore, M = √3M₀/2.