Re: Potential gradient between two spheres?

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Antonio Carlos M. de Queiroz" <acmdq@xxxxxxxxxx>

Tesla list wrote:
> Original poster: "Denicolai, Marco" <Marco.Denicolai@xxxxxxxxxxx>
> Hi Antonio,
> I have got your two references (A. Russell from 1911) but they just
> allow to calculate the capacitance between two spheres A and B at
> potential Va and Vb. I want to know the potential at a point X between
> the two spheres. How to do that?
> Should I simply replace the two spheres with two point charges Qa and Qb
> of value given by the Russell paper and then calculate by their
> superimposition the resulting potential at X?
> Best Regards
> P.S. Sorry for my question but I'm still a beginner with electrostatics.

Two point charges would work if the distance between the spheres is
much larger than their diameters. The exact solution can be found
with an infinite series of point charges placed at certain points
along the line that passes trough the centers of the spheres. This
is the "image" method. The exact procedure was developed by Lord
Kelvin, and appears in his works. See the references in Russel's
paper. I have implemented a calculation in my program Inca, using
rings, but it is not suitable for a closed-form formula.

Antonio Carlos M. de Queiroz