A bar magnet is 8 cm long. At a distance of 3 cm from its centre in the broadside-on position, the magnetic field is measured to be 4 10⁻⁶ T . Determine the pole strength of this magnet.

Step-by-step solution

Given: Length of the magnet, 2l = 8 cm l = 4 cm = 0.04 m Distance from the centre, d = 3 cm = 0.03 m Magnetic field, B = 4 10⁻⁶ T The magnetic field at a distance d on the equatorial line (broadside-on position) of a bar magnet is given by: B = ₀ 4 M (d^2 + l^2)^ 3/2 where M = m 2l is the magnetic moment and m is the pole strength. Substituting the given values: 4 10⁻⁶ = 10⁻⁷ m 0.08 ((0.03)^2 + (0.04)^2)^ 3/2 4 10⁻⁶ = 10⁻⁷ m 0.08 (0.0009 + 0.0016)^ 3/2 4 10⁻⁶ = 10⁻⁷ m 0.08 (0.0025)^ 3/2 4 10⁻⁶ = 10⁻⁷ m 0.08 (0.05)^