Force between two oppositely charged conducting spheres

AI Thread Summary
The discussion centers on the force between two oppositely charged conducting spheres, emphasizing that at large distances, the force behaves similarly to that between point charges due to the radial symmetry of charge distribution. It is noted that while this approximation holds true, the conductance of the spheres becomes negligible at such distances. Participants suggest that a thorough analysis would involve considering point-like charges and dipole correction terms, indicating a deeper examination of the charge distribution is necessary. The problem is framed as an exercise in solving Laplace's equation under specific boundary conditions related to the spheres being equipotential surfaces. Overall, the conversation highlights the complexities involved in accurately modeling the interaction between charged conducting spheres.
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...if the spheres are separated by a large distance - one with charge Q, the other with charge -Q - isn't the force between them just the same as the force between two oppositely charged point charges, since the electric field produced by one of the spheres "looks like" the field of a point charge to the other sphere?
 
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If the charge distribution on each sphere is radially symmetric, the force between is the same as for two point charges. If they are conducting spheres, this is approximately true at large distances.
 
Hi Axiom
The charge distribution is radially symmetric only at very large distances. There is an exact solution in Smythe "Static and Dynamic Electricity", 3rd Edition, page 128-129.
Bob S
 
"Large distances" would also make conductance of spheres insignificant.

If this was an exam problem in a serious Electrodynamics course, I'd give an answer as the force from point-like charges + the dipole correction terms. That seems to be what the "conducting spheres" is hinting at.
 
K^2 said:
"Large distances" would also make conductance of spheres insignificant.

If this was an exam problem in a serious Electrodynamics course, I'd give an answer as the force from point-like charges + the dipole correction terms. That seems to be what the "conducting spheres" is hinting at.

I'm not sure that would be enough..

If it were a serious question, I would assume the problem was to evaluate the charge distribution of two charged spheres, each in the others field.
The only information you have is that the spheres are equipotential surfaces...
We're looking for a solution to Laplace's equation in three dimensions with the stated boundary condition.
Probably not difficult to anyone rather more clever than I. :biggrin:
 
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