**Author:**

Tombe, Frederick David

**Category:**

Research Papers

**Sub-Category:**

Mechanics / Electrodynamics

**Date Published:**

February 24, 2020

**Keywords:**

Maxwell's displacement current, aether, vortices, electromagnetism, electromagnetic radiation, electromagnetic wave equation, displacement current, wireless telegraphy, magnetization, linear polarization, electron-positron aether

**Abstract:**

Ampère’s Circuital Law is the most controversial of Maxwell's equations due to its association with displacement current. The controversy centres around the fact that Maxwell’s entire physical basis for introducing the concept of displacement current in the first place, was the existence of a dense sea of molecular vortices pervading all of space. The modern-day physical parameter known as the electric permittivity, ε, being reciprocally related to the dielectric constant, is historically rooted in the elasticity of this medium. Indeed, the dielectric constant served as the vehicle through which the speed of light was imported into the analysis from the 1855 Weber-Kohlrausch experiment, yet the medium itself has since been totally eliminated from the textbooks. In order to understand how the omission of Maxwell’s vortex sea has impacted upon electromagnetic theory, this article will examine the relationship between Ampère’s Circuital Law in its differential form and the curl of the Biot-Savart Law with which it is generally equated. In particular the continued use of displacement current in the dynamic state, despite the omission of its original physical basis, will be contrasted with the omission of displacement current in the steady state version of Ampère’s Circuital Law as it applies in space.

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