Focaloid

A Fokaloid is a geometric figure that by mutually confocal ellipses ( 2D) or ellipsoids (3D) is bounded.

Mathematical definition ( 3D)

If a boundary by an implicitly given ellipsoid

Described with the half-shafts, the second boundary is by

Given.

In the limiting case of one speaks of thin, in the other case of thick Fokaloiden.

Confocality

Confocal ellipsoids have the same foci or foci, which by the above example

Are given.

Definition fokaloide distribution

A confocal or fokaloide distribution occurs when, for example, the layers of constant density of mass distribution or the layers of the same charge density by confocal ellipsoids or ellipses (see picture) are given.

Physical meaning

Fokaloide also have significance in the physical potential theory. It lies in the fact that two confocal homogeneously filled with mass or charge ellipsoids bring in an outside environment specimens forces that point in the same direction and are proportional to the respective masses and charges of each individual ellipsoids.

From this one can conclude that various confocal homogeneously filled with mass or charge Fokaloide same mass or charge cause the same effect regardless of their geometry outside their expansion.

This also means that the external effect of a fokaloiden distribution by the outer effect of this confocal homogeneously filled with the same mass ellipsoid can be written.

Furthermore, can the external field of a route ( thin rod ) with it describe homogeneously distributed mass or constant potential along the rod as fokaloide distribution, the ends of the track ( the rod ) are the foci ( focuses ) of fokaloiden field. The field vectors are perpendicular to the ellipsoid same field amount.