Electric fields inside a series of curved corners

The 2-dimensional electric fields internal to five different corner configurations made from three conductors are investigated. These corners are such that the sections in the plane considered consist of two semi-infinite straight lines at right angles joined by a conductor which is part of a circular arc. By methods involving conformal transformations, complex inversion and elliptic integrals, exact solutions giving the electric intensity are obtained. Graphs are given showing the variation of electric intensity along the conductor surfaces, and also along the axis of symmetry where appropriate. The results should be useful in assessing the effects of rounding off corners in electrical constructions. The same theory, with suitable change of symbols, gives the magnetic fields of the configurations. Also the results, with small modifications, may be applied to calculate the mechanical forces.