Electrostatic patch effects in Casimir force experiments performed in the sphere-plane geometry

Abstract

Patch potentials arising from the polycrystalline structure of material samples may contribute significantly to measured signals in Casimir force experiments. Most of these experiments are performed in the sphere-plane geometry, yet, up to now all analysis of patch effects has been taken into account using the proximity force approximation which, in essence, treats the sphere as a plane. In this paper we present the exact solution for the electrostatic patch interaction energy in the sphere- plane geometry, and derive exact analytical formulas for the electrostatic patch force and minimizing potential. We perform numerical simulations to analyze the distance dependence of the minimizing potential as a function of patch size, and quantify the sphere-plane patch force for a particular patch layout. Once the patch potentials on both surfaces are measured by dedicated experiments our formulas can be used to exactly quantify the sphere-plane patch force in the particular experimental situation.

13 pages, 4 figures

References in corpus (12)

• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• Surface energies, work functions, and surface relaxations of low index metallic surfaces from first-principles
• Observation of the thermal Casimir force
• Scaling and Suppression of Anomalous Quantum Decoherence in Ion Traps
• Simplified motional heating rate measurements of trapped ions
• A microscopic model of electronic field noise heating in ion traps
• Surface Contact Potential Patches and Casimir Force Measurements
• Temporal Extent of Surface Potentials between Closely Spaced Metals
• Measurement of the short-range attractive force between Ge plates using a torsion balance
• Modeling electrostatic patch effects in Casimir force measurements
• Energy shifts of Rydberg atoms due to patch fields near metal surfaces
• A quick test of the WEP enabled by a sounding rocket

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