Energy conversion with Active Dipoles*

To understand the creation of electromagnetic energy (or a photonic degree of freedom) from an external energy source, an electromotive force must be generated capable of separating positive and negative charges. The separation of charges (free or bound) may be modelled as a permanent polarization, which has a non-zero electric vector curl, created by an external force per unit charge, or fictitious electric field. The resulting system forms an active physical dipole in the static case, or an active Hertzian dipole in the time dependent case. This system is the electrical dual of the magnetic solenoid described by a magnetic vector potential and excited by an electrical current. Correspondingly, the creation of an active electric dipole is a voltage source may be described by an electric flux density, which exhibits an electric vector potential and a magnetic current boundary source, within the frame work of two-potential theory without the need for the existence of the magnetic monopole. From this result we derive the Dual electric Berry phase and make the conjecture that it should be equivalent to the geometric phase that is described in modern electric polarization theory, which also describes the nature of the permanent polarization of a ferroelectric or triboelectric material. This work gives a formal meaning to the electric vector potential that defines the etectric geometric phase, and determines that a permanent polarization output voltage has both a scalar and vector potential component, which must be considered to fully describe the nature of an active electric dipole. Additionally, we show that Faraday's and Ampere's law may be derived from the time rate of change of the Aharanov-Bohm phase and the DAB phase respectively, independent of the electromagnetic gauge.