Electromagnetic energy changes due to charges moving through constant, or zero, magnetic field

The author examines the interaction between a charge q moving at constant velocity through a region in which the magnetic flux density may be zero, but the A vector is not. The simplest example of the source of A is a closed toroid carrying constant current. The motion of q induces an EMF in the toroid, causing an exchange of energy with the current source, although the toroid produces no external magnetic flux or induced electric field. It is shown that the apparent anomaly of a transfer of energy without a force on q is resolved by the changes of internal energy and by the definition of what is meant by the term ´force´. Assigning the momentum and stored energy to the charges, clarifies the operating principle, defines the parameters in terms of inductance, and provides an equivalent circuit, as in other electrical machines. The Aharonov-Bohm effect, which is commonly stated to be inconsistent with classical electromagnetism, provides an example of the momentum change in terms of the quantum-mechanical phase change due to the vector A.