Recent interest in problems in higher space dimensions
is becoming increasingly important
and attracted the attention of many investigators
in variety of fields in physics. In this paper,
the electrostatic energy of two geometries (a
charged spherical shell and a non-conducting
sphere) is calculated in higher space dimension,
N. It is shown that as the space dimension increases,
up to N = 9, the electrostatic energy of
the two geometries decreases and beyond N = 9
it increases. Furthermore, we discuss a simple
example which illustrates classical renormalization
in electrostatics in higher dimensions.