Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I am trying to run a simulation, and I have come across a theoretical question.

Let's say that you have an electric charge producing a potential on a conducting surface (let's assume it's infinite). Now, if you make a crack in the surface so that there is a gap (filled with air for example), you create an area where the current can't pass through.

The equations say that the potential inside the crack will change because of the different electric permitivity, while on the other side it won't be affected at all.

My problem is how the current is supposed to move. If I just integrate for the current density I can get the current vectors on the surface:

[tex]V=\frac{1}{4\pi\epsilon}\frac{Q}{r}[/tex]

[tex]E=-\nabla{V}=\frac{1}{4\pi\epsilon}\frac{Q}{r^2}[/tex]

[tex]J=\sigma E[/tex]

[tex]I=\int{J\cdot dA}[/tex]

, but they look like they would without the crack, with the exception that no current passes through the crack.

Current moves along the electric field, which, in my case, just has a gap where the crack is, and its shape is otherwise unaffected.

I know that current is supposed to go around the crack, much like a fluid would, so I probably need a boundary condition for the crack. Does anybody know how I should go about it???

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# Electric potential and current around an insulator

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