On the Shape Dependence of the Tangential Casimir Force

TL;DR

This paper investigates how the shape of a rack gear influences the tangential Casimir force, revealing that small shape changes significantly affect the tangential component while leaving the normal force nearly unaffected.

Contribution

It provides a numerical analysis demonstrating the shape dependence of the tangential Casimir force under ideal boundary conditions.

Findings

Tangential Casimir force is highly shape-dependent.

Normal Casimir force remains nearly unchanged with shape variations.

Small shape modifications cause significant changes in tangential force.

Abstract

The normal and tangential Casimir force for the rack gear is calculated numerically in the case of ideal boundary conditions for the electromagnetic field - perfect reflection on the boundaries. The resulting tangential force appears to be essentially shape dependent. Relatively small shape variations lead to the essential changes in tangential force, whereas normal force remains almost unchanged.