Electrostatic interaction between a cylinder and a planar surface

 An exact analytical expression for the potential energy of the electrostatic interaction between a plate-like particle 1 and a cylindrical particle 2 of radius a2 immersed in an electrolyte solution of Debye–Hückel parameter κ is derived on the basis of the linearized Poisson–Boltzmann equation without recourse to Derjaguin's approximation. Both particles may have either constant surface potential or constant surface charge density. In the limit of κa2→0, in particular, the interaction between a plate with zero surface charge density and a cylinder having constant surface charge density becomes identical to the usual image interaction between a line charge (a charged rod of infinitesimal thickness) and an uncharged plate.