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mmwave

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Textbooks point out that to use Gauss' Law successfully there must be geometric symmetry that makes the Efield constant over some reasonable surface. I thought this was just to make the math tractable but then I noticed the following issue.

1. Point charge inside a thin spherical shell of a different dielectric constant. You can calculate the Efield inside without any knowledge of the shell using Gauss' Law.

2. Point charge near a planar dielectric boundary. You must know the distance from the charge to the boundary and both dielectric constants to calculate the Efield on the charge side of the boundary.

In one case you only need to know about the region of interest, in the second case you need to know everything. Is symmetry alone the difference?

For the spherical shell I can see that the field due to any polarization charge will 'cancel out' inside the shell and so the Efield is the same as if there were no shell. What about other cases? How about an infinite planar charge and a parallel dielectric boundary?