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 (with N≥3). The very short argument is essentially based on the application of Reynold's transport theorem in connection with the Green–Stokes integral representation formula for smooth functions on bounded domains of , which permits to reduce the N-dimensional problem to a one-dimensional one. Owing 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.
- Received March 21, 2016.
- Accepted May 27, 2016.
- © 2016 The Author(s)
Published by the Royal Society. All rights reserved.