Electric field in asymmetric conductor configuration
I was trying to figure out an electrostatics exercise. I am confortable solving these type of problems, when there is an easy application of symmetrical properties and Gauss's Law. But this one took me by surprise. As the picture shows, there is a spherical surface with charge +q, as well as the ellipsoidal surface. Both are conductors and hollow, without any type of contact between them. The figure shows a cross section of the configuration, showing qualitatively that they are not centered at the same point, but still the ellipsoidal axis passes right through the center of the sphere shell.
I don't have to calculate the field in all space. All I must do is order the points A,B,C and D in increasing order of electric field. I am stucked because it seems to me that I don't have the tools to contemplate the charge redistribution problem.
If we were dealing with static charges it would be quite easy to realize that the superposition principle applies inmediately. Maybe it is easier if I try to imagine different steps to achieve this distribution. First I imagined an empty spherical shell, with an homogeneus charge distribution throughout it's surface. 903
Using Gauss we would get that the field inside is zero. Later we would add the ellipsoidal. And here is when I ask myself, the charge distribution of the spherical shell at a first instant doesn't affect the ellipsoidal one. The latter creates an electric field that would reaccomodate the spherical charges. After this I am not sure of what could be said about the field inside the sphere.
It is not zero between the ellipsoidal and the sphere. But it is indeed zero inside the ellipsoidal. Inmediately outside the ellipsoidal the field is normal to the surface.
I must say also, that the exercise asks to calculate the external field to the sphere, which I suspect is the same as if there was a sphere charged with $+2q$. This hunch is product of the way the question is being asked. If this is true it would be very nice to know why since it is inconclusive what happens after the "redistribution time".
Hope the doubt is clear enough. Thanks for reading. 903