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.

 

[astrokreng]

for any insights or guidance.

I am familiar with the concept of a dielectric sphere in a uniform electric field. However, I have not come across a problem where the uniform electric field is replaced by a dipole field. This would certainly be an interesting problem to explore.

In order to solve this problem, one approach could be to use the method of images. This involves creating a virtual image of the dipole outside the sphere and considering the combined effect of the actual and virtual dipole on the sphere. This approach has been used in similar problems and may provide an explicit solution for the resultant field.

Another approach could be to use numerical simulations or computational methods to model the behavior of the dipole field in the presence of the dielectric sphere. This would allow for a more accurate and detailed analysis of the problem.

I would recommend consulting with a textbook on electromagnetism or a research paper on a similar problem to gain a better understanding of the topic and potential approaches for solving it. Additionally, reaching out to other scientists or researchers in the field may provide valuable insights and guidance. Good luck with your exploration of this interesting problem.