  Simple analytic expressions for the polarizability of metallic nanoparticles
are in wide use in the field of plasmonics, but their origins are not obvious.
In this article, expressions for the polarizability of a particle are derived
in the quasistatic limit in a manner that allows the physical origin of the
terms to be clearly seen. The discussion is tutorial in nature, with particular
attention given to the role of particle shape since this is a controlling
factor in particle plasmon resonances.
