Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/195
If are the surface-densities on the opposed surfaces of a solid
sphere of radius , and a spherical hollow of radius , then If
and be the whole charges of electricity on these surfaces, The
capacity of the enclosed sphere is therefore . If the outer
surface of the shell be also spherical and of radius , then, if
there are no other conductors in the neighbourhood, the charge
on the outer surface is Hence the whole charge on the inner
sphere is and that of the outer If we put , we have the case of
a sphere in an infinite space. The electric capacity of such a
sphere is , or it is numerically equal to its radius. The
electric tension on the inner sphere per unit of area is The
resultant of this tension over a hemisphere is normal to the
base of the hemisphere, and if this is balanced by a surface
tension exerted across the circular boundary of the hemisphere,
the tension on unit of length being , we have