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 = ${\displaystyle {\mu }_0 (\text{H}+\text{M})}$     ...(i)

${\displaystyle \therefore \text{M}=\frac{\text{m}}{\text{V}}=\frac{0.5}{1\times {10}^{-6}}}$

∴ M = 0.5 × 10⁶ A/m

∴ B = ${\displaystyle {\mu }_0 (0.5\times {10}^4+0.5\times {10}^6)}$   ...[From (1)]

∴ B = ${\displaystyle {\mu }_0 (0.5\times {10}^4+50\times {10}^4)}$

∴ B = ${\displaystyle {\mu }_0 (0.5+50)\times {10}^4}$

∴ B = ${\displaystyle 4\pi \times {10}^{-7}\left(50.5\right)\times {10}^4}$

∴ B = ${\displaystyle 4\times 3.14\times 50.5\times {10}^{-3}}$    ...[π = 3.14]

∴ B = 0.634 Wb/m²