"Corner" electrodynamic force

The electrodynamic force acting on current carrying straight filiform conductors can be easily calculated by using the formulas based on the work of Laplace. It is much more difficult to evaluate the force acting on the corner part of bent conductors or in contacts, where the distance between the conductors becomes zero and the above-mentioned formulas cannot be used any more. In the paper, by using a conformal mapping and a formula for inductance calculation, we analyze two typical cases: the bent broad flat conductor (two-dimensional model) and the bent round conductor (three-dimensional model). We propose practical formulas to evaluate the force acting on the corner part of the conductors, considering the nonuniform distribution of direct current density.