Dielectric Sphere in Electric Dipole

[Apteronotus]

Hi,

I am aware that the effects of a dielectric sphere in a uniform electric field have been done in many introductory electromagnetism books.

Is anyone ware of a similar problem where the uniform electric field is replaced by a dipole field?
Would solving such a problem for the resultant field have an explicit solution?

If anyone could direct me to a resource, or advise me as to how to approach the problem I would greatly appreciate it.

Thanks in advance

 

[Meir Achuz]

A dielectric sphere in the field of a point charge is done in advanced textbooks using a Legendre polynomial expansion.
The sphere in the field of a dipole can be done in a similar manner, but is much more complicated. It is a bit simpler if the sphere is located on the axis of the dipole.
The dipole field would have to be expanded in LPs about a point on its axis.
Another approach is to take the result for two charges, +q and -q, a distance d apart.
Then take the limit as d-->0.