Potential of a dipole with actual physical extension?

[Gavroy]

I think everybody here knows the equation that gives the potential of a point like dipole, but how does the field look like if you have e.g. a metal sphere with radius $R$ and a certain dipol moment, how does this potential look like?

 

[DrDu]

If the surface charge varies like cos theta, the field outside will equal to that of an ideal dipole in the center of the sphere. Inside the sphere, the field is constant. Using Coulombs law it is easy to work out the actual field configuration.