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**Conducting Sphere "shielding" an electric field**

Hello. I have a question regarding a problem that I have seen printed many times in various books and which I saw on a test today:

A hollow conducting sphere contains 2 charges, [tex] q_1\;and\;q_2 [/tex]. Outside the sphere are two additional charges, [tex] q_3\;and\;q_4 [/tex]. Which charges determine the properties of the field within the sphere?

The answer, as is often printed, is that just the first two charges contribute to the field.

The traditional explanation of this answer involves Gauss's Law-- only the first two charges are enclosed within the conducting sphere, and so the divergence of the field there thus only relies upon those two sources.

After reflection, I recently realized that this cannot possibly be correct, since equal-field Gaussian surfaces can be arbitrarily produced.

What is the real reason for this? I would prefer a more intuitive, qualitative reason, although math is pretty cool too. I'm guessing that the specific way in which [tex] q_3\;and\;q_4 [/tex] redistribute the charge on the conducting sphere somehow results in a null field within, but I can't for the life of me figure out how the fact that the sphere is conducting allows for shielding.

Thanks in advance

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