A bar magnet with a length of 1 cm and a cross-sectional area of 1.0 cm ^2 creates a magnetic field of 1.5 10⁻⁴ T at a point in the end-on position, located 15 cm away from its centre. Calculate the magnetic field B at the centre of the magnet.

Step-by-step solution

The magnetic field at the end-on position of a short bar magnet is B_ axial = ₀ 4 2M d^3 . Substituting the given values: 1.5 10⁻⁴ = 10⁻⁷ 2M (0.15)^3 M = 1.5 10⁻⁴ 0.003375 2 10⁻⁷ 2.53 A m ^2 The volume of the magnet is V = A l = (1.0 10⁻⁴) 10⁻² = 10⁻⁶ m ^3 . The magnetization I is: I = M V = 2.53 10⁻⁶ = 2.53 10^6 A/m The pole strength m is: m = M l = 2.53 10⁻² = 253 A m The magnetic intensity H at the centre due to the two poles (at a distance l/2 = 0.5 10⁻² m each) is directed opposite to the magnetization: H = -2