Macroscopic Coulomb Force Versus Maxwell Stress Theory: Consistencies and Discrepancies

In macroscopic electrostatics, there are two rivaling concepts describing the electrostatic action of force: the continuous formulation of the Coulomb force and the Maxwell stress theory. Although their mutual consistency is well‐known for free charges distributed continuously on volumes and surfaces, a revisit of the seemingly uncontroversial problem of a conducting elliptic cylinder subjected to an external electric field discloses an oddity in the limiting case of a vanishing semi‐minor axis. After an in‐depth investigation of this limiting case, for which the cylinder turns into a sheet, the oddity proves to be a contradiction whose resolution reveals one of the approaches as the richer concept of broader validity. The far‐reaching consequences of this result are eventually elucidated analytically by two established textbook problems, and promising points of departure for further investigations are delineated.