Question

Assume that each iron atom has a permanent magnetic moment equal to 2 Bohr magnetons (1 Bohr magneton equals 9.27 × 10⁻²⁴ A m²). The density of atoms in iron is 8.52 × 10²⁸ atoms m⁻³. (a) Find the maximum magnetisation I in a long cylinder of iron (b) Find the maximum magnetic field B on the axis inside the cylinder.

Answer 1

Given:-

No of atoms per unit volume, f = 8.52 × 10²⁸ atoms/m³

Magnetisation per atom, M = 2 × 9.27 × 10⁻²⁴ A-m²

(a) Intensity of magnetisation, \[I = \frac{M}{V}\]

⇒ I = 2 × 9.27 × 10⁻²⁴ × 8.52 × 10²⁸

⇒ I = 1.58 × 10⁶ A/m

(b) For maximum magnetisation ,the magnetising field will be equal to the intensity of magnetisation.

So, I = H

Magnetic field (B) will be,

B = 4π × 10⁻⁷ × 1.58 × 10⁶

⇒ B ≈ 19.8 × 10⁻¹ = 2.0 T