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Assuming a stable, static status, we use Gauss's law:

Let's assume we're discussion a sphere, even though it works for every shape, it's just to simplify things.

If I wrap the inside of the sphere, I will get 0 electric field flow through my "wrapper", because if I had an electric field, it wouldn't have been a static, stable status.

So I keep making bigger and bigger wrappers, almost touching the edges of the sphere, but still no electrical field, which implies no electric charge in the wrapper (aka, inside the conductor). When I place the wrapper outside of the conductor, I find that there is an electrical field. which implies it can only be on the outer surface.

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