The interaction of a small object with surrounding plasma is an area of plasma-physics research with a multitude of applications. This paper introduces the plasma octree code pot, a microscopic simulator of a spheroidal dust grain in a plasma. pot uses the Barnes–Hut treecode algorithm to perform N-body simulations of electrons and ions in the vicinity of a chargeable spheroid, employing also the Boris particle-motion integrator and Hutchinson's reinjection algorithm from SCEPTIC; a description of the implementation of all three algorithms is provided. We present results from pot simulations of the charging of spheres in magnetised plasmas, and of spheroids in unmagnetized plasmas. The results call into question the validity of using the Boltzmann relation in hybrid PIC codes.