Homoeoid

Homoeoid

Discussion

Encyclopedia
A homoeoid is a shell bounded by two concentric, similar
Similarity (geometry)
Two geometrical objects are called similar if they both have the same shape. More precisely, either one is congruent to the result of a uniform scaling of the other...

ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...

s (2D) or ellipsoids(3D).
When the thickness of the shell becomes negligible, it is called a thin homoeoid.

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
Potential
*In linguistics, the potential mood*The mathematical study of potentials is known as potential theory; it is the study of harmonic functions on manifolds...

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.