• Corpus ID: 118513882

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

@article{Patla2012SmallAA,
  title={Small Angle Approximation for Non-parallel Plate Capacitors with Applications in Experimental Gravitation},
  author={Bijunath R. Patla},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2012}
}

• B. Patla
• Published 14 August 2012
• Physics
• arXiv: General Relativity and Quantum Cosmology

An approximate analytical formula for the capacitance of a non-parallel plate capacitor with small values of inclination angles and distance separations of the plates is presented. Most applications involving position sensing or stabilizing the proof masses of precision gravity experiments (for example, testing the equivalence principle) often use a parallel plate approximation for modeling the capacitance, which in turn, is used for estimating the noise. The analytical approximation presented here is based on the more general, but hard to implement, formalism for small angles given in Xiang (2005). Our approximation is accurate and reliable in the small-angle limit because it does not involve elliptic integrals of the rst kind that has an indeterminate value at unity. Our formalism is very useful for computing the forces acting on the proof masses simply by taking the derivative of the capacitance. Eects of varying the inclination angle, plate dimension, and distance separation on the value of the capacitance per unit length are analyzed in detail. We use the formula derived in this paper to compute the acceleration of the proof mass due to the presence of sensing electrodes (used for positioning the proof masses) with an assumed tilt of 10 6 rad as applicable to SR-POEM: an experiment aiming to test the weak