Features of the configurations "small particle -plate" and "plate -plate" in the theory of fluctuation electromagnetic interaction

TL;DR

This paper examines the differences between 'small particle -plate' and 'plate -plate' configurations in fluctuation electromagnetic interaction theory, highlighting the limitations of transitioning between these models and their implications for theoretical generalizations.

Contribution

It reveals that the transition from 'plate -plate' to 'small particle -plate' configurations is not straightforward, impacting the validity of certain theoretical approaches.

Findings

The transition from 'plate -plate' to 'small particle -plate' is not continuous.

Existing solutions for 'small particle -plate' can validate generalizations of 'plate -plate' theory.

The study clarifies the limitations of applying geometrical limits in fluctuation electromagnetic interactions.

Abstract

It is shown that the limiting transition from the geometrical configuration "plate -plate" to configuration "small particle -plate" being frequently used in the theory of Lifshitz -Pitaevskii, is not continually true. On the other hand, the known solution to the problem in the last configuration can be used to verify the generalizations of the theory being worked out in the former configuration.