Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials

An active electrical network contains a voltage or current source that creates electromagnetic energy through a method of transduction that enables the separation of opposite polarity charges from an external source. The end result is the creation of an active dipole with a permanent polarisation and a non-zero electric vector curl. The external energy input impresses a force per unit charge within the voltage source, to form an active physical dipole in the static case, or an active Hertzian dipole in the time dependent case. This system is the dual of an electromagnet or permanent magnet excited by a circulating electrical current or fictitious bound current respectively, which supplies a magnetomotive force described by a magnetic vector potential with a magnetic geometric phase proportional to the enclosed magnetic flux. In contrast, the active electric dipole may be described macroscopically by a circulating fictitious magnetic current boundary source described by an electric vector potential with an electric geometric phase proportional to the enclosed electric flux density. This macroscopic description of an active dipole is an average description of some underlying microscopic description exhibiting emergent nonconservative behaviour not found in classical conservative laws of electrodynamics. We show that the electromotive force produced by an active dipole must have both electric scalar and vector potential components to account for the magnitude of the voltage it produces. Following this we analyse an active cylindrical dipole in terms of scalar and vector potential and confirm that the electromotive force produced, and hence potential difference across the terminals is a combination of vector and scalar potential difference depending on aspect ratio of the dipole.