Electrostatic stress: insightful analysis and manipulation of Maxwell's stress equation for electrostatics

Maxwell's stress equation for electrostatics identifies a tensile stress in the direction of the electric field and a pressure normal to this direction. For an isolated, spherically symmetric static charge distribution, Maxwell's stress equation is manipulated using a variant of Stokes' Theorem. The recast stress equation eliminates the stress normal to the electric field and establishes a stress only aligned with the electric field. For two separated, spherically symmetric static charge distributions, Maxwell's stress equation is also manipulated using a variant of Stokes' Theorem. The recast stress equation develops a line stress that only exists on the straight path between the two charge distributions. The analysis and manipulation of Maxwell's stress equation provides some insight into electrostatic stresses and establishes additional tools for the electrical engineer when analyzing electrostatic system stresses.