Patch Effect in Cylindrical Geometry: The Step Accelerometer

The actual distribution of charges on a metal does not guarantee its surface to be equipotential because of the impurities and microcrystal structure of the material. This phenomenon, known as patch e↵ect, is responsible for the mutual force and torque between two metallic surfaces at a finite distance. Patch e↵ect is important for any precision measurement whose set-up includes conducting surfaces in a closed proximity to each other. This is particularly true for the Satellite Test of the Equivalence Principle experiment where the di↵erential motion of cylindrical test masses will be used to test the universality of free fall to an unprecedented accuracy of about 1 part in 1018.