In certain circumstances, the force on a secondary conducting body carrying induced eddy currents can be calculated from the gradient of effective inductance, measured in the primary circuit at the operating frequency. Uncertainty as to the exact circumstances is resolved by an approach through matrix algebra. Either the self parameters of the secondary impedance matrix must be constant, or the secondary circuits must be effectively resistanceless. In the resistanceless case, the theory extends to cover multiple primary circuits, but not otherwise. The theory is verified by application to the single-phase induction motor, and other physical implications are discussed.