English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We present exact closed-form expressions and complete asymptotic expansionsfor the electrostatic force between two charged conducting spheres of arbitrarysizes. Using asymptotic expansions of the force we confirm that evenlike-charged spheres attract each other at sufficiently small separation unlesstheir voltages/charges are the same as they would be at contact. We show thatfor sufficiently large size asymmetries, the repulsion between two spheres$\textit{increases}$ when they separate from contact if their voltages or theircharges are held constant. Additionally, we show that in the constant voltagecase, this like-voltage repulsion can be further increased and maximised thoughan optimal $\textit{lowering}$ of the voltage on the larger sphere at anoptimal sphere separation.

Exact closed-form and asymptotic expressions for the electrostatic force between two conducting spheres