To effectively model this for arbitrary geometry, it is necessary to numerically solve Poisson's equation:
This is accomplished by successive over-relaxation (SOR) of the
three-dimensional finite difference approximation of the diffusion
equation, which Poisson's equation is a steady-state solution of.
Doing this calculation gives the full values of the potential in the
vicinity of the objects in question. Given
it is possible to calculate the charge on each of the objects
and from that, and the known potential between each pair of objects
(
More details of the electrostatic model used
can be found in Chapter
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