A bar magnet, having a length of 1 cm and a cross-sectional area of 1.0 cm ^2 , generates a magnetic field of 1.5 10⁻⁴ T at an end-on position located 15 cm from its centre. Determine the magnetic moment M of the magnet.

Step-by-step solution

The magnetic field at an axial (end-on) position of a short bar magnet is given by: B = ₀ 4 2M d^3 Since the length of the magnet l = 1 cm is much smaller than the distance d = 15 cm , the short magnet approximation is valid. Substituting the given values: 1.5 10⁻⁴ = 10⁻⁷ 2M (0.15)^3 M = 1.5 10⁻⁴ (0.15)^3 2 10⁻⁷ M = 1.5 10^3 0.003375 2 M = 5.0625 2 M 2.5 A m ^2