Mistake in Magnetostatics?

NGSolve
1

Dear Developers of Netgen, NGSolve,
I have a question regarding the Magnetostatics tutorial with beziercurves:
https://docu.ngsolve.org/latest/i-tutorials/wta/coil.html?highlight=potential%20problem

I am relatively new to NGSolve and also have not the deepest understanding of Electromagnetics.

My question is the influence of the electric conductivity of the copper wire on the B-field distribution.

When I use the implemented tutorial and change the value of sigma i always get the same B-field distribution. To me this does not make sense as with an increased conductivity of the coil material the generated B-field should be stronger.

It seems like sigma canceles out due to its implementation in the BilinearForm (Potential Problem for solving current density) and its implementation in the LinearFrom (curl curl Problem for the B-field) resulting in the same B-field distribution.

Any help or clarification would be highly appreciated.

Kind Regards
Michael

2

To me this does not make sense as with an increased conductivity of the coil material the generated B-field should be stronger.

An increase in the coil current would results in a stronger B-field. In the example the current density is prescribed as a boundary condition and thus is current flowing through the coil is independent on the conductivitiy. Thus the B-field remains same.

lff = LinearForm(1/crosssection*psi*ds("in")).Assemble()

However, you will see that with a larger conductivity the potential value on the boundary “In” should be smaller, as a smaller potential difference is required to drive the current.

Hope that helps.

Paul