# Time harmonic Maxwell's low f

Hi,

I’m trying to solve for the magnetic field in time harmonic Maxwell’s for low frequency (50 Hz). I have a coil with alternating current and above the coil I have a metal plate, from which I want to get the magnetic field from the induced eddies. The solution I get does not look as expected, but I’m not sure what my error is.
I have started from this example Maxwell Equations — NGS-Py 6.2.2402 documentation
which is a magnetostatic case. I then changed the magnetostatic equation

\int \mu^{-1} \operatorname{curl} u \operatorname{curl} v = \int j v,

to the time harmonic for low f:

\int i \omega\sigma uv + \int \mu^{-1} \operatorname{curl} u \operatorname{curl} v = \int j v

I also changed the finite element space to nograds=False and added complex = True:

fes = HCurl(mesh, order = 3, dirichlet=“outer”, nograds = False, complex = True)

I hope that someone can find my error or perhaps provide a similar example. My file is attached.

/Richard
maxwell_coil_AC.ipynb (5.5 KB)

I could not find any mistaake in your model.

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My solution looks different, or maybe I make some mistake when I plot the solution. Is your imag(B) the same as my curl(u).imag?

Thanks!

I exported the results to vtk and plotted in paraview and then it looks fine, but still I would be happy to know what mistake I made when plotting in jupyter.

Ah, there seems to be an issue with small values and complex values in vector plots in the webgui. As a workaround you can draw real and imaginary part of B field in uT or nT:

Draw (1e9 * curl(u).imag, mesh, "B-field", draw_surf=False, \
clipping = { "pnt" : (0,0,0), "vec" : (0,1,0), "function" : False }, autoscale=False, min=0, max=0.01,
vectors = { "grid_size" : 100 })


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