E&M : Simulate/Calculate B field due to J

[Hepth]

My end goal is to analytically or numerically calculate the magnetic field inside and around a square conductor that has connection points at the top and bottom with a voltage applied.

Are there any software packages (mathematica, or even just C) that can do this given ANY current density in the conductor? The problem is that the conducting square does not have uniform conductivity, and can, in theory, have gradients, dead spots, etc, thus creating some eddy currents or some asymmetry that I cannot calculate easily by hand, hence numerical simulation would be perfect.

An example would be : a square conductor with leads at top and bottom. Some voltage is applied. The square conductor is split in two where the left side is rho_1 resistivity and right side is rho_2.

This specific one I think I can numerically do IF the leads connected the entire top, then its just integrate contributions from a number of line segments and you're done. But if the geometry of conductance is not simple I get stuck.

tldr: Any good simulation/numerical calculation for B fields given a specific current density equation.

 

[Vanadium 50]

Most people I know with this problem use Ansys. It's commercial, and I understand not cheap.

 

[Born2bwire]

What frequency range and physical sizes are we talking about here?

 

[marcusl]

Do you need the field close to the conductor? Farther away, the details of the current density are irrelevent.

 

[Hepth]

Yes, I need all ranges with no approximation, including fields in parts of the conductor due to currents in other parts. No frequency range, can be a static current, about an amp, resistance varies, physical dimensions should be irrelevant as processes should scale.

 

[marcusl]

physical dimensions should be irrelevant as processes should scale.

Your statement isn't clear. This is a static current? Because if it's AC, eddy currents are scale dependent.

 

[Born2bwire]

If it's AC, you might want to look into NEC (Numerical Electromagnetics Code) which is a wire MOM code. If it's just static currents then... well you could always write your own code to deal with it. A lot of books that deal with electromagnetics and method of moments will discuss some kind of static case though usually it's in terms of charge via the Poisson equation. But I also think you could easily just use the Biot-Savar Law. You can get an approximation of the current by finding the equivalent resistance of each section of the wire and treating it like a circuit problem and then using the solved currents as uniform currents over the surface of the conductor. Then you can integrate over the currents as given by Biot-Savart for an infinitesimal current element.