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Multiscaled asymptotic expansions for the electric potential: surface charge densities and electric fields at rounded corners. (English) Zbl 1126.78004
The authors compute the charge density and electric field topology at sharp and rounded tips of electrodes by solving the Poisson equation for the electrostatic potential subject to proper Dirichlet boundary condition and a required asymptotic behaviour at infinity. They derive asymptotic expressions for the electric potential at the vicinity of the electrode tip that are suitable for further applications. The theoretical results are compared with numerical solutions in Cartesian as well as in cylindrical geometry with axial symmetry.

MSC:
78A30 Electro- and magnetostatics
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