Consider a spherical shell of finite
width, with inner radius a and outer radius b.
A total charge Q is distributed uniformly over the
volume of this shell. Find the electric field E(r)
for all positions r, i.e. inside the hollow of the shell,
r<a, within the thickness of the shell, a
<r<b, and outside the shell, b<r.
Make a sketch of |E| vs. r. Discuss what happens in
the limit that a approaches b, and the thickness
vanishes, while Q is kept constant.
This problem is meant to help you think about how
a two dimensional surface charge density can be thought of as
a limit of a three dimensional volume charge density.
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