Capacitor and rod paradox

Abstract

In this article we deal with a paradox, in the sense of apparent contradiction, of the theory of Special Relativity: an U-shaped circuit, with an opening $L_0$ and with a charged capacitor, moves relative to a conductive rod of length $L_0$. The question is: seen from a referential in the circuit and then viewed from a reference point on the rod, does the circuit close discharging the capacitor or not? The solution to the paradox, which seems to involve only the issue of length contraction, actually also involves the issue of simultaneity, as we have shown. The article, in addition to presenting and solving the paradox, reviews important points of the theory of Special Relativity, such as geometric representation of Lorentz transformations, simultaneity and desynchronization of clocks along an object in movement.

Keywords:
Relativity; paradoxes; simultaneity