Question

16. A bar of an iron -silicon alloy having the B-H behavior shown in the Figure is inserted within a coil of wire 0.40 m long and having 50 turns, through which passes a current of 0.1 A. (a) What is the B field within this bar? (b) At this magnetic field, (i) What is the permeability?i) What is the relative permeability? (i What is the susceptibility? (iv) What is the magnetization? Magnetic field strength, H (oersteds) 0.2 0.4 0.6 15,000 1.4 1.2 10,000 1.0 0.8 공 0.6 5,000 0.4 0.2 0.0 60 10 20 30 40 50 Magnetic field strength, H (A/m) Flux density, B (tesla) N Flux density, B (gauss)

Answer 1

Given N = 50 I = 0.1 A L = 0.40 m Therefore Magnetic field strength = NI/L A/m Therefore H = 50 times 0.1/0.4 = 12.5 AT/m From the plot: at H = 12.5 AT/m Corresponding magnetic field = 1.0 Tesla Permeability (mu) = B/H Therefore mu = 1.0/12.5 = 0.08 Therefore mu_0 mu_r = 0.08 Therefore mu_r (Relative Permeability) = 0.08/mu_0 where mu_0 = 4 pi times 10^-7 Therefore mu_r = 0.08/4 pi times 10^-7 = 63661.977 Now relationship between susceptibility and permeability mu = mu_(1 + chi_m): where chi_m = Susceptibility Therefore chi_m = mu/mu_0 - 1 Therefore chi_m = 0.08/4 pi 10^-7 -1 = 63660.997 \r\n Magnetization = chi_H Therefore M = chi_H Therefore M = 63660.997 times 12.5 Therefore M = 795762.2125 A/m

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