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arXiv · 1505.04970

The Newtonian Potential and the Demagnetizing Factors of the General Ellipsoid

Giovanni Di Fratta
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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 $N \geqslant 3$). 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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Giovanni Di Fratta. 2016-03-20. The Newtonian Potential and the Demagnetizing Factors of the General Ellipsoid. https://doi.org/10.1098/rspa.2016.0197

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