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The self-capacitance of a sphere is calculated from the potential
of a point charge q.
A.1 Self Capacitance of a Sphere
This potential has spheres as equipotential surfaces, with the center of the
spheres identical to the location of the point charge. Thus, if one
inserts a conducting sphere with its center at the location of the point
charge the field outside the sphere will not change, since the surface of
the conductor coincides with an equipotential surface of the field. The
self-capacitance is therefore
with d the diameter of the sphere.