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A dielectric sphere in an external field. Consider a simple dielec-
tric with permittivity e, in the form of a uniform spherical ball of radius a. It
is placed at the origin in an external electrostatic potential (x, y, z) = bxy
(where r, y, z are Cartesian coordinates and b is a constant). Find the elec-
trostatic potential o and electric field E everywhere.
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