Permeability in ferromagnetic material (AC)

[godel maxwell]

Homework Statement

The following coil-wound core (core length = L , Gap length = lg, cross- sectional area = A , core permeability = only hysteresis graph is given, N = N turns) is driven by a Voltage source, is known that the current in the coil is 60hz AC.

Determine
(a.) the time -varying magnetic current
(b.) the time -varying voltage
(c.) the time -varying Magnetic flux (core and gap)
(d.) Max current

Homework Equations

The Attempt at a Solution

https://scontent-atl1-1.xx.fbcdn.net/hphotos-xft1/v/t34.0-12/11393075_1647223932163354_8775291292436932394_n.jpg?oh=a9e06bc69260df62ffe0db9745e5cb17&oe=557848C4 [/B]
What I have done is to first calculate v(t) looking up the Bmax in the hysteresis loop, then I have substituted that value in the above equation v(t), then I have calculated the current using H=NI/L, again I got Hmax from the hysteresis loop in order to obtain Imax.
I don´t know how to continue: how to express the flux and B in terms of t if the permeability is not a constant.
Thank you for your help!

 

[s k gupta]

varying permeability means varying inductance of the circuit and thus varying magnetizing current. If only hysteresis curve is given we should use it to determine nonlinear permeability and thus H and B field. We can take H field to be purely sinusoidal and thus determine not-so-perfect sinusoidal B field in-turn determining the flux.