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Floating conductors with fixed potential difference

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Hi,
I'm trying to model a conductive instrument placed in an electric field (I'm interested in the electric field flux through a few boundaries of the instrument). To model this conductor, I've applied the floating potential boundary condition on its entire surface.
However, I now want to keep one part of this instrument (call it P1) at a +1V potential difference to the rest of the instrument, and I can't seem to implement this properly.

I tried applying an electric potential boundary condition on P1 with the value 1+aveop1(V), where aveop1 is an "average component coupling" that I've defined on the remaining instrument area. But in this case, the solution does not converge. I'm guessing this is because the electric potential on P1 changes the floating potential which then again changes the potential on P1 and so on.

I have also tried to first run the simulation using a floating potential and recorded the resulting instrument potential V_ins. I then changed the floating to an electric potential with V_ins as its value, and on P1 chose the potential V_ins+1. Is this the appropriate method I should use? I feel like its not really correct, since I now ignore the effects of this potential difference completely when I specify the potential of the instrument. Instead, maybe I should use two separate floating potentials and link them using some constraint?

I also noticed that I get slightly different results when I use the electric potential boundary condition with V_ins on the entire instrument, compared to when I use the floating potential on it. Shouldn't they be the same? Or have I missed something here?

In summary, is it possible to specify the potential of one object, based on the floating potential of another? If so, how would I implement this?
Now that I think about it, it is possible that I have defined my geometry in a weird way, so that them having different potentials make no physical sense causing this non-convergence. But ignoring this, how could this problem be solved in principle?

Thank you for your time,
Konrad

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