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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.
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Solution
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
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