A bar magnet has a length of 1 cm and a cross-sectional area of 1.0 cm ^2 . It generates a magnetic field of 1.5 10⁻⁴ T at a point in the end-on position, 15 cm away from its centre. Determine the magnetization I of the magnet.

Step-by-step solution

Given, length of the magnet, 2l = 1 cm = 10⁻² m Cross-sectional area, A = 1.0 cm ^2 = 10⁻⁴ m ^2 Magnetic field at end-on position, B = 1.5 10⁻⁴ T Distance from the centre, d = 15 cm = 0.15 m Since d 2l , the magnetic field at the end-on (axial) position of a short bar magnet is given by: B = ₀ 4 2M d^3 Substituting the given values: 1.5 10⁻⁴ = 10⁻⁷ 2M (0.15)^3 M = 1.5 10⁻⁴ 3.375 10⁻³ 2 10⁻⁷ M 2.53 A m ^2 The volume of the magnet is: V = A 2l = 10⁻⁴ 10⁻² = 10⁻⁶ m ^3 The magnetization I is defined as the magnetic mom