The quantity of electricity on a planetary ellipsoid maintained at potential
in an infinite field, is
|
(37)
|
where
is the equatorial radius, and
is the polar radius.
If
, the figure is a circular disk of radius
, and
|
(38)
|
|
(39)
|
152.] Second Case. Let
, then
and
,
|
(40)
|
and the equation of the hyperboloids of revolution of two sheets becomes
|
(41)
|
The quantity
becomes reduced to
, and each of the hyperboloids of one sheet is reduced to a pair of planes intersecting in the axis of
whose equation is
|
(42)
|
This is a system of meridional planes in which
is the longitude.
The quantity
becomes
, whence
, and the equation of the family of ellipsoids is
|
(43)
|
These ellipsoids, in which the transverse axis is the axis of revolution, are called Ovary ellipsoids.
The quantity of electricity on an ovary ellipsoid maintained at a potential
in an infinite field is
|
(44)
|
If the polar radius is
, and the equatorial radius is
,
|
(45)
|