Dielectric Screening in a Spherical Cavity

In this work we examine the electrostatic screening potential due to a point charge located off-centre in a spherical dielectric cavity. This potential is expanded for the case in which the dielectric constant $\epsilon$ is large, several methods of finding the terms in the expansion are investigated, and closed-form expressions are found through third order in $\epsilon$ along with error bounds. Finally, possible uses of these expressions in molecular dynamics simulations of isolated charged molecules is discussed.