A bar magnet of length 1 cm and cross-sectional area 1.0 cm^2 produces a magnetic field of 1.5 × 10^-4 T at a point in end-on position at a distance 15 cm away from the centre. (a) Find the magnetic moment M of the magnet. (b) Find the magnetization I of the magnet. (c) Find the magnetic field B at the centre of the magnet.

Sol. (a) Given d = 15 cm = 0.15 m l = 1 cm = 0.01 m A = 1.0 cm^2 = 1 x 10^-4 m^2 B = 1.5 x 10^-4 T M = ? We know B ⃗ = μ base 0/ 4π x 2Md/(d^2 – l^2)^2 ⇒ 1.5 x 10^-4 = 10^-7 x 2 x M x 0.15/ (0.02255 – 0.0001)^2 = 3x 10^-8M / 5.01x 10^-4 ⇒ M = 1.5 x 10^-4 x 5.01 x 10^-4/3x 10^-8 = 2.5 A (b) Magnetisation I = M/V = 2.5 / 10^-4 x 10^-2 = 2.5 x 10^6 A/m (c) H = m/4πd^2 = M/ 4πId^2 = 2.5/ 4 x 3.14 x 0.01 x (0.15)^2 net H = H base N + H = 2 x 884.6 = 8.846 x 10^2 B ⃗ = μ base 0 (-H + I) = 4π x 10^-7 (2.5 x 10^6 – 2 x 884.6) ≈ 3,14 T