双和单电容器佯谬
Two and single superconductive capacitor paradox
摘要：
本文研究了两电容佯谬的一个新的版本，具体地说，当所有的电容器极板、导体和开关都是由同一种材料制成时，它的一种更简单的形式称为单电容佯谬。在非稳态区（温度高于临界温度），电路具有非零的剩余电阻，由此可以解释单电容放电引起的闭合电路初始电场能量的降低。(Also将假定在所述电路内任何剩余电感都可以有效地忽略）。但在临界状态下（当温度小于临界值时），电路完全不保持任何剩余电阻，我们考虑随后出现的情况。根据伦敦定律，闭路中的电场能量在其初始值和零之间振荡，这似乎代表了一个新的单（双）电容器悖论（电场能量振荡）。准确地说，它表明，在这里的电荷和电流谐波振荡在时间以这种方式提到的电路可以被认为是一个典型的LC电路的电感定义的超导性，即伦敦参数和电容器特性。这样，电容器可变电场和电流可变磁场的总能量保持恒定，这代表了上述悖论的解决方案。
英文摘要：
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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