0
$\begingroup$

Consider Poisson equation $\nabla \cdot (\sigma(x)\nabla u)=0$ in a domain $D$, where $\sigma(x)$ is the spatially dependent conductivity. On the boundary we have $n$ electrodes (Dirichlet BC $u=\text{const}$ on each electrode). And the rest of the boundary is insulating material $du/d\vec n=0$ (Neumann BC). The electrodes do not have any contact impedance.

Is it possible to derive the Poisson equation for this system based on a microscopic description of electrons behaviour, they repel eachother and are attracted to electrodes? Eg. From Coloumbs law and Newtons law

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

This is indeed possible. See the derivation at https://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity

Improve this answer
$\endgroup$