A A question about current density in finite element analysis

AI Thread Summary
When dealing with multiple current sources in finite element analysis, it is essential to determine how to apply Maxwell's equations correctly. The discussion highlights the need to calculate the current densities from all independent sources and consider their superposition when analyzing magnetic potential, especially in ferromagnetic materials. It emphasizes that the response of ferromagnetic materials can significantly exceed the original source from free currents, complicating the analysis. Simplifying assumptions may be necessary depending on the geometry, particularly in transformer applications. Overall, this problem is complex and requires careful consideration of multiple factors in the analysis.
JH_1870
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I know that if there is only one conductor providing the current density, then the current density can be used.

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But if you apply Maxwell's equation when there are multiple current sources, I don't know which value to use.

This is not an analysis using a tool, but a problem when I develop the code myself.

Should I calculate all the values for multiple independent sources and then add them up?

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Where J is the applied current density. Is it correct to use the applied current density when calculating the magnetic potential in the iron core?

And, when there are several applied current densities, is it necessary to apply the superposition principle to solve them?
 
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This appears to be a very non-trivial problem that you are trying to solve. For problems with ferromagnetic materials, sometimes the geometry involved leads to simplifying assumptions, particularly in the case of transformers. You might find some good reading in this thread, along with some of the "links" that are referenced: https://www.physicsforums.com/threads/magnetic-flux-is-the-same-if-we-apply-the-biot-savart.927681/
For the general case of magnetic materials with currents in conductors, I think it may be a very difficult problem that you are trying to tackle.
 
Just an additional comment or two: This type of problem can not be solved as a perturbation with a small response and source generated from the ferromagnetic material. Instead, in many cases, the response of the ferromagnetic material may be many and many times larger than the original source from the free currents in the conductor. Perhaps others may also comment, but this is my take on this problem.
 
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