Ampère’s Circuital Law and Displacement Current

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Ampère’s Circuital Law is the most controversial of Maxwell 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, is historically rooted in the elasticity of this medium, yet the medium itself has been totally eliminated from the textbooks. In order to understand how the omission of Maxwell’s vortex sea has impacted on 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.'s_Circuital_Law_and_Displacement_Current