Abstract
Any polyhedron accommodates a type of potential theoretic skeleton called a mother body. The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov [1] and developed by Bjorn Gustafson and Makoto Sakai [2]. In this paper, we attempt to apply the brilliant idea of mother body to Electrostatics to compute the potentials of electric fields.
Highlights
Open AccessA mother body for a heavy body in geophysics is a concentrated mass distribution sitting inside an object, providing the same external gravitational field as the body
We explore the mother bodies for convex polyhedra, assuming that any convex polyhedron preserves a unique mother body called a skeleton
If Ω is a bounded domain in Rn provided with a mass distribution ρΩ (e.g., Lebesgue measure restricted to Ω ), another mass distribution μ sitting in Ω and producing the same external Newtonian potential as ρΩ is called a mother body of Ω, provided it is maximally concentrated in mass distribution and its support has Lebesgue measure zero [3]
Summary
A mother body for a heavy body in geophysics is a concentrated mass distribution sitting inside an object (body), providing the same external gravitational field as the body. The problem of finding mother bodies is related to constructing a family of bodies that generate the same potential as a distributed mass. It was studied by many mathematicians and physicists like Zidarov [1], Gustafsson [2] [3], Sakai [2] and others.
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