# Two and single superconductive capacitor paradox

Vladan Pankovic

Arxiv ID: 0912.0648•Last updated: 1/2/2023

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.

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