8. A sphere of radius R1 carries a uniform chargedensity p throughout its volume except
for a small spherical hollow volume of radius R2 located at distance a from the center
(and fully contained within the larger sphere).

a) Calculate the electric field E at the center of the hollow sphere. [Be careful, you can't
just apply Gauss's law here. Qenclosed may be zero, but you can't do the surface integral.
The field is NOT zero.
b) Calculate the potential at the same point.

Solution Preview

You should have in your textbook(s) or lecture notes or previous homework derived the formula for the electric field and potential created by a (single) uniformly charged sphere.
However, just in case, you can also find these formulae at web page http://www.phys.uri.edu/~gerhard/PHY204/tsl94.pdf

From these formula we need the following:
A uniformly charged sphere of radius R and charge density ρ creates electric field ...

Solution Summary

This solution calculates an electric field and potential at the center of a hollow sphere

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