How to get mechanical work from a capacitor and two batteries

TL;DR

This paper analyzes how mechanical work can be extracted from a capacitor and batteries by changing the plate separation under different conditions, demonstrating a cycle that yields net work.

Contribution

It provides a simple, general physics analysis of extracting mechanical work from a capacitor-battery system during cyclic operations.

Findings

Net mechanical work can be obtained from a cycling capacitor under certain conditions.

The work depends on whether the capacitor is held at constant charge or voltage.

The analysis is accessible for teaching in general physics courses.

Abstract

The work done by a parallel plate capacitor is evaluated when the plate separation is changed. Two cases are considered: 1) the capacitor has a constant charge; 2) the capacitor is at constant voltage. The net work is calculated when the device follows a closed cycle in the charge-voltage space. For certain conditions a net mechanical work can be obtained from the cycling capacitor. The analysis is simple enough to be explained in a general physics course.