Solving the Landau-Lifgarbagez-Gilbert Equation for Ferromagnetism

[dorker]

I'm trying to work out how fast I can switch an electromagnet's polarity, assuming I know the properties of the core's material. The magnetization dynamics are described by the Landau-Lifgarbagez-Gilbert equation (dM/dt = -ℽMxHeff + λMx(MxHeff), which is quite a chore to solve, seeing as it uses the effective field Heff, which also has M as one of its variables.

But this book I'm reading, Physics of Ferromagnetism by Sochin Chikazumi, simply uses the applied H field instead of effective H, which makes the equation tremendously easier to solve. The thing is, it does so with no explanation. Is this a valid approach, and what assumptions does it take?

On a side question, the same book describes the relationship between the magnetization vector M and flux density B as B = M + µ0H, whereas wikipedia (can't post link, but the magnetization article ) says it's B = µ0(H + M). How does that work, are the µ's different or something?

 

[marcusl]

Switching polarity of a large electromagnet is almost always limited by the winding. The time constant, of course, is L/R. Trying to force too rapid a change (dI/dt too large) will create an emf that exceeds the breakdown voltage of the windings. The core will most likely follow the coil without slowing you down.

 

[dorker]

Thanks!