Definite solution of the two capacitor paradox (and two water bucket paradox)

TL;DR

This paper presents a straightforward solution to the two capacitor paradox, showing that energy loss is due to work done by electric fields, and illustrates this with a mechanical water bucket analogy.

Contribution

It offers a simple, ideal circuit explanation for the paradox and introduces a mechanical analogy to clarify the energy transfer process.

Findings

Electrical field energy loss equals work done by electric fields.

No dissipation processes are necessary for energy loss in ideal circuits.

Mechanical analogy with water buckets illustrates the energy transfer concept.

Abstract

In this work we suggest very simple solution of the two capacitors paradox in the completely ideal (without any electrical resistance or inductive) electrical circuit. Namely, it is shown that electrical field energy loss corresponds to works done by electrical fields of both capacitors by movement of the electrical charge. It is all and nothing more (some dissipation processes, e.g. Joule heating and electromagnetic wave emission effects) is necessary. Additionally, we shortly demonstrate a simple mechanical analogy of mentioned paradox and its solution. Concretely we consider two water buckets connected by a valve where is a seeming loss of the gravitational potential energy that can be explained by the work in the gravitational field.