(Answered) Uniform field in a cavity a sphere has radius r1 and

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Uniform field in a cavity **

A sphere has radius R1 and uniform volume charge density ρ. A spherical cavity with radius R2 is carved out at an arbitrary loca- tion inside the larger sphere. Show that the electric field inside the cavity is uniform (in both magnitude and direction). Hint: Find a vector expression for the field in the interior of a charged sphere, and then use superposition.

What are the analogous statements for the lower-dimensional analogs with cylinders and slabs? Are the statements still true?

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