Two and single superconductive capacitor paradox

TL;DR

This paper explores a new version of the superconductive capacitor paradox, demonstrating that in the superconducting state, electric energy oscillates harmonically between electric and magnetic forms, conserving total energy.

Contribution

It introduces a novel interpretation of the superconductive capacitor paradox, showing energy oscillations in an ideal LC circuit without residual resistance, based on London law.

Findings

Electric field energy oscillates between initial value and zero in superconductive regime.

Electric charge and current oscillate harmonically, forming an ideal LC circuit.

Total energy remains constant during oscillations.

Abstract

In this work we consider a new version of the remarkable two capacitor paradox, concretely its simpler form called single capacitor paradox in realistic case when all capacitors plates, conductors and switch are made by the same kind of superconductive material. In non-superconductive regime (when temperature is larger than critical) electric circuit holds non-zero residual electric resistance by means of which decrease of the initial electric field energy in closed circuit by single capacitor discharge can be explained. (Also it will be supposed that within mentioned electric circuit any residual inductivity can be effectively neglected.) But in superconductive regime (when temperature is smaller than critical) electric circuit exactly does not hold any residual resistance and we consider what then appears. It is shown that here, according to London law, electric field energy in closed circuit oscillates during time between its initial value and zero what seemingly represents new single (two) superconductive capacitor paradox (of electric field energy oscillation). Precisely, it is shown that here electric charge and current harmonically oscillate during time in such way that mentioned electric circuit can be considered as a typical LC circuit with inductivity defined by superconductivity, i.e. London parameter and capacitor characteristics. In this way total energy of the capacitor variable electric field and electric current variable magnetic field stands constant which represents solution of mentioned paradox.