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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.
Contents
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.
References
Homoeoid Wikipedia(Text) CC BY-SA