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

An approximate analytical formula for the capacitance of a non-parallel platecapacitor with small values of inclination angles and distance separations ofthe plates is presented. Most applications involving position sensing that areemployed in precision experiments and micromechanical devices often use aparallel plate approximation for modeling the capacitance. The analyticalapproximation presented here is based on the more general, but hard toimplement formalism for small angles, and that may be used directly to computethe forces acting on the proof masses by taking the derivative of thecapacitance.  Effects of varying the inclination angle, plate dimension and separation onthe value of the capacitance per unit length are analyzed in detail. We use theformula derived in this paper to compute the acceleration of the proof mass dueto the presence of sensing electrodes (used for positioning the proof masses)with an assumed tilt of $\sim 10^{-6}$ rad as applicable to SR-POEM: anexperiment aiming to test the weak equivalence principle - a fundamentalpostulate of general relativity.

Small Angle Approximation for Non-parallel Plate Capacitors with Applications in Experimental Gravitation