Calculating Magnetic field of permanent magnet

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Calculating the magnetic field around permanent magnets involves understanding the superposition of magnetic fields, particularly in configurations like bar magnets. Resources on Maxwell's equations often focus on current-induced fields, leaving a gap in information for permanent magnets. The challenge includes accounting for interactions between magnets, such as hysteresis and saturation effects, which complicate the calculations. A small dipole's magnetic moment can be influenced by nearby dipoles, requiring consideration of induced moments based on external fields and susceptibility. For simulation purposes, pre-calculating the magnetic field and superposing it with wire-generated fields may be a viable approach, but careful attention to magnet interactions is essential.
Hobnob
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Hi: I'm having real trouble finding resources for the problem of accurately calculating (and drawing the field lines for) a magnetic field around a permanent bar magnet, or between two permanent magnets (I assume this is the same problem, as fields are superposable). I've found lots of sites talking about Maxwell's equations, but nothing about how to relate this to permanent magnets, rather than fields induced by currents. For that matter, I'm a little lost even with Maxwell's equations, as my field calculus is *very* rusty and was never that good to start with... I can't quite see how to move between the path/surface integrals and the actual field at a particular point.

Can anyone point to some good resources for someone who needs a bit of hand-holding but is ultimately up to the task?

All this is ultimately to be part of a motor/generator simulator, so a final question is: can I manage by just pre-calculating the magnetic field and superposing it on the field from the wire, or am I barking up completely the wrong tree?

Thanks
 
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in first approximation the field well outside the magnet is a usual dipole field.
The next step is quite troubling, because you need to take into the account the effect of one part magnet on the magnetization of another part of the magnet. The problem is that you may have hysteresis und saturation. I have now idea how take the hysterisis into the account, but saturation is fine, as soon as you are using a computer.
The problem may be formulated like this:
let's imagine we have a small dipole with a magnetic moment M. Then, if we put another dipole near it, their magnetic field will be a superposition of two dipoles. But their dipole moments will be affected by the external magnetic field from another dipole. The additional induced magnetic moment will be proportional to the external magnetic field and the dipole's supsceptibility, which may be nonlinear function of the external magnetic field.
 

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