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An active electrical network contains a voltage or current source thatcreates electromagnetic energy through a method of transduction that enablesthe separation of opposite polarity charges from an external source. The endresult is the creation of an active dipole with a permanent polarisation and anon-zero electric vector curl. The external energy input impresses a force perunit charge within the voltage source, to form an active physical dipole in thestatic case, or an active Hertzian dipole in the time dependent case. Thissystem is the dual of an electromagnet or permanent magnet excited by acirculating electrical current or fictitious bound current respectively, whichsupplies a magnetomotive force described by a magnetic vector potential with amagnetic geometric phase proportional to the enclosed magnetic flux. Incontrast, the active electric dipole may be described macroscopically by acirculating fictitious magnetic current boundary source described by anelectric vector potential with an electric geometric phase proportional to theenclosed electric flux density. This macroscopic description of an activedipole is an average description of some underlying microscopic descriptionexhibiting emergent nonconservative behaviour not found in classicalconservative laws of electrodynamics. We show that the electromotive forceproduced by an active dipole must have both electric scalar and vectorpotential components to account for the magnitude of the voltage it produces.Following this we analyse an active cylindrical dipole in terms of scalar andvector potential and confirm that the electromotive force produced, and hencepotential difference across the terminals is a combination of vector and scalarpotential difference depending on aspect ratio of the dipole.

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