The magnetic circuit of figure and Problem 1.6 has the

The magnetic circuit of figure and Problem 1.6 has the

The magnetic circuit of figure and Problem 1.6 has the following dimensions:
Ac = 8.2cm2 lc = 23cm
lp = 2.8 cm g = 0.8 mm
X0 = 2.5 cm N = 430 turns
a. Assuming a constant permeability of Âľ = 2800Âľ0, calculate the current required to achieve a flux density of 1.3 T in the air gap when the plunger is fully retracted (x = 0).
b. Repeat the calculation of part (a) for the case in which the core and plunger are composed of a nonlinear material whose permeability is given by where Bm is the magnetic flux density in the material.
c. For the nonlinear material of part (b), use MATLAB to plot the air-gap flux density as a function of winding current for x — 0 and x = 0.5X0.

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