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 = $\frac{M}{V}$
$\Rightarrow$I = 2 × 9.27 × 10⁻²⁴ × 8.52 × 10²⁸
$\Rightarrow$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 = 4$\mathrm{\pi }$ × 10⁻⁷ × 1.58 × 10⁶
$\Rightarrow$B ≈ 19.8 × 10⁻¹ = 2.0 T.