Finding potential of a dipole outside of a sphere

[nicholasBourbaki]

TL;DR

What is the potential of a dipole outside of a sphere when the orientation of the dipole is tangent to the sphere?

Hey guys! I am currently tackling the following problem: An electric dipole P is kept close to a conducting grounded sphere of radius A -assume a distance B between the center of the sphere and dipole. What is the potential of the dipole outside of the sphere when the orientation of the dipole is tangent to the sphere?

I tried finding the green function of the structure and then tried to find the electric dipole in terms of two volume charged density and finally tried to find the potential using these two values. However that did not get me anywhere. I would appreciate if someone could point me to the right direction.

 

[Baluncore]

Welcome to PF.

Just an idea, but I would look at the reflection of the dipole in the conductive-mirror surface of the sphere. Analyse the dipole and its image. The image of the dipole is distorted by the surface curvature, and will be reversed.

There may be a simplification, but you have not specified the relative length of the dipole to the diameter of the sphere.

 

[Meir Achuz]

If you model the dipole as a plus charge and a minus charge, a distance d apart, you can find the field of each charge by the usual image calculation.