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Question
A rod of magnetic material of cross-section 0.25 cm2 is placed in a magnetizing field of intensity 4000 A/m-1. The magnetic flux passing through the rod is 25 × 10-6 Wb. Find out
(a) relative permeability
(b) magnetic susceptibility and
(c) magnetisation of the rod.
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Solution
Given: A = 0.25 cm2 = 25 × 10-6 m2
H = 4000 A m-1, Φ = 25 × 10-6 Wb
Magnetic induction is
B = `phi/"A"`
`= (25 xx 10^-6)/(25 xx 10^-6)`
= 1 Wb/m2
(a) B = μ0μrH
∴ The relative permeability of the material,
`mu_"r" = "B"/(mu_0"H")`
`= 1/(4 xx 3.142 xx 10^-7 xx 4000)`
`= 10000/50.272`
= 198.91 = 199
(b) `mu_"r" = 1 + chi_"m"`
∴ The magnetic susceptibility of the material,
`chi_"m" = mu_"r" - 1`
= 199 - 1
= 198
(c) `chi_"m" = "M"_"z"/"H"`
The magnetization of the rod,
`"M"_"z" = chi_"m""H" = 198 xx 4000 = 7.92 xx 10^5`A/m
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