Force between two oppositely charged conducting spheres

[AxiomOfChoice]

...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?

 

[Meir Achuz]

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.

 

[Bob S]

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

 

[K^2]

"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.

 

[AJ Bentley]

"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.