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The Derivation of Maxwell's Displacement Current

Author:

Tombe, Frederick David

Category:

Research Papers

Sub-Category:

Mathematical Physics

Language:

English

Date Published:

May 26, 2025

File:

/Research Papers-Mathematical Physics/Download/10203

Downloads:

130

Keywords:

Maxwell's displacement current, aether, linear polarization, electron-positron sea, precession, EM radiation, angular acceleration

Abstract:

An undergraduate student learning about Maxwell’s equations for the first time is typically shown, that with the exception of a part of one of these equations, they can be derived from first principles with reference to nineteenth century experiments. The exception referred to relates to the displacement current term in Ampère’s Circuital Law. While the existence of displacement current can be justified retrospectively due to its role in the derivation of the electromagnetic wave equations, it’s very difficult to present from first principles, a concise theoretical proof of its existence. The normal textbook method is to justify its existence in connection with the conservation of electric charge in a charging or discharging capacitor, but the major problem with this method is that the displacement current term that is so derived is not the term that is used in the derivation of the electromagnetic wave equations. The textbook derivation is that of a term involving the electrostatic E field, while the E field that is involved in electromagnetic radiation arises from time-varying electromagnetic induction. The important question of how to derive the latter kind of displacement current will be the focus of this article.