Question

When a plate of magnetic material of size 10 cm × 0.5 cm × 0.2 cm (length, breath, and thickness respectively) is located in a magnetizing field of 0.5 × 10⁴ A/m^-1, then a magnetic moment of 0.5 Am² is induced in it. Find the magnetic induction in the plate.

Answer 1

Data: μ₀ = 4π × 10^-7; l = 10 cm, b = 0.5 cm, h = 0.2 cm, H = 0.5 × 10⁴ Am^-1, m = 0.5 Am²

The volume of the plate,

V = l × b × h

V = 10 × 0.5 × 0.2

V = 1 cm³ ⇒ 1 × 10^-6 m³

B = `mu_0  ("H" + "M")`     ...(i)

`therefore "M" = "m"/"V" = 0.5/(1 xx 10^-6)`

∴ M = 0.5 × 10⁶ A/m

∴ B = `mu_0  (0.5 xx 10^4 + 0.5 xx 10^6)`   ...[From (1)]

∴ B = `mu_0  (0.5 xx 10^4 + 50 xx 10^4)`

∴ B = `mu_0  (0.5 + 50) xx 10^4`

∴ B = `4pi xx 10^-7 (50.5) xx 10^4`

∴ B = `4 xx 3.14 xx 50.5 xx 10^-3`    ...[π = 3.14]

∴ B = 0.634 Wb/m²