Question: Let the space between two concentric spheres with radii a and R a be filled uniformly with charge. (a) Calculate the total energy U

Let the space between two concentric spheres with radii a and R ≥ a be filled uniformly with charge.

(a) Calculate the total energy UE in terms of the total charge Q and the variable x = a/R. Check the a = 0 and a = R limits.

(b) Minimize UE with respect to x (keeping the total charge Q constant). Identify the physical system which achieves the minimum you find.

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