Homoeoid

A homoeoid is a shell (a bounded region) bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D).
When the thickness of the shell becomes negligible, it is called a thin homoeoid. The name homoeoid was coined by Lord Kelvin and Peter Tait.

Mathematical definition
If the outer shell is given by

with semiaxes  the inner shell is given for  by

.

The thin homoeoid is then given by the limit

Physical meaning
A homoeoid can be used as a construction element of a matter or charge distribution. The gravitational or electromagnetic potential of a homoeoid homogeneously filled with matter or charge is constant inside the shell. This means that a test mass or charge will not feel any force inside the shell.

See also
Focaloid

References

External links

Category:Surfaces
Category:Mathematical physics
Category:Potentials