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Electrostatics of two charged spheres at small separation
Song, Yi Wilkerson, Blake
Song, Yi
Wilkerson, Blake
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URCAS, Student research, 2018 Spring, Class of 2018, Physics, Department of, Electrostatics, Number theory, Lambert series
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Abstract
There are many examples of electrostatic phenomena in our daily lives, from those as simple as the sparks that accompany the taking off of our sweaters, to the formation of clouds and rain droplets. Moreover, electrostatics are widely used in modern industry, such as laser printing and
automotive spray painting. Our research project focuses on analyzing the electrostatic interaction
between two charged conducting spheres in the limit when they are about to touch each other. By
using analytical techniques, we obtain dimensionless expressions of capacitances for those two
spheres. Furthermore, we derive the electrostatic force between two spheres. When the two
spheres are of the same size, our results show that the electrostatic force can be expressed as a
linear combination of two parts, one is always attractive and the other one is always repulsive.
The attractive part always dominates the repulsive part at sufficiently small distances, thus the
electrostatic force is always attractive at small distances, even for positively charged spheres!
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Presentation by Yi Song ('18) and Blake Wilkerson delivered at the Rhodes College Undergraduate Research and Creative Activity Symposium (URCAS).