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I am trying to solve the complex form of poisson equation ∇[ε(x)∇V(x)] = -1/εo ρ(x)

with complex permittivity.

If I introduce complex permittivity ε = εr - j σ/(εow), then I must introduce a complex potential ,V = Vr + jVi.

That means the charge density, ρ, must also take a complex form, but I'm not sure what to make of that.

For my boundary conditions, I have the real part of the voltage measured from the oscilloscope, and the real charge density I compute through the conservation equations.

Any help on this topic? I can't find much on this on internet.

Thanks!

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# Complex form of poisson equation

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