The Newtonian Potential and the Demagnetizing Factors of the General Ellipsoid

Abstract

The objective of this paper is to present a modern and concise new derivation for the explicit expression of the interior and exterior Newtonian potential generated by homogeneous ellipsoidal domains in ${\mathbb{R}}^N$ (with $N⩾3$). The very short argument is essentially based on the application of Reynolds transport theorem in connection with Green-Stokes integral representation formula for smooth functions on bounded domains of ${\mathbb{R}}^N$, which permits to reduce the N-dimensional problem to a 1-dimensional one. Due to its physical relevance, a separate section is devoted to the the derivation of the demagnetizing factors of the general ellipsoid which are one of the most fundamental quantities in ferromagnetism.

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