Electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) play a pivotal role in many of the cutting edge experiments in plasmonics. EELS and CL experiments are usually supported by numerical simulations, which-though accurate-may not provide as much physical insight as analytical calculations do. Fully analytical solutions to EELS and CL systems in plasmonics are rare and difficult to obtain. This paper aims to narrow this gap by introducing a new method based on transformation optics that allows to calculate the quasistatic frequency- and time-domain response of plasmonic particles under electron beam excitation. We study a nonconcentric annulus (and ellipse in the Supporting Information ) as an example.