Mathematical analysis for predicting an unbalanced force in a simple asymmetric circuit using Maxwellian electrodynamics

The notion of inertia is not explicitly supported in Maxwellian electrodynamics, as there is no reaction to the Lorentz force in the Lorentz relation. Recent experimental work suggests that the apparent lack of reaction to rail gun firing indicates a violation of the Newtonian laws of motion, but Einsteinian and Newtonian electrodynamics do support the principle of inertia and its consequence, the law of conservation of momentum. In this paper, drawing from first principles in electrical engineering and Euclidean geometry we construct the integrals that describe the forces upon the line elements of a simple asymmetric circuit caused by its current and that same current´s local magnetic self-induction caused by the other line elements. The complete solutions of these double integrals produce complex mathematical expressions, indicating imbalance of forces. The possibility of an entirely new class of electric motors for energy generation and motion arises with the constant change in linear momentum for the body with flow of high current within a geometrically asymmetric embedded circuit.