Does a Dielectric Sphere in a Uniform Electric Field Exhibit Azimuthal Symmetry?

[luisgml_2000]

Homework Statement

A solid sphere is placed in an otherwise uniform electric field. Its upper half is made up from a material with dielectric constant e_1; the other half has dielectric constant e_2. The plane at which the parts of the sphere intersect is parallel to the uniform field at infinity.

The problem is to find the potential at every point in space.

Homework Equations

The Attempt at a Solution

My only question is: is there any way for this problem to have azimuthal symmetry?

I tried to put the z axis parallel to the field at infinity, but I think it's not right since I don't get the solution.

 

[dynamicsolo]

...The plane at which the parts of the sphere intersect is parallel to the uniform field at infinity.

My only question is: is there any way for this problem to have azimuthal symmetry?

If I'm reading this right, it sounds like the external field is perpendicular to the symmetry axis of the dielectric sphere. I think that effectively abolishes the azimuthal symmetry.