Laplace boundary-value problem in paraboloidal coordinates

L. Duggen, Morten Willatzen, L. C. Lew Yan Voon

Research output: Contribution to journalJournal articleResearchpeer-review


This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a boundary-value problem on a paraboloidal surface. In spite of the complex nature of the former, it is shown that the latter solution can be quite simple. Results are provided for the equipotential surfaces and electric field lines are given near a paraboloidal conductor.
Original languageEnglish
JournalEuropean Journal of Physics
Issue number3
Pages (from-to)689-696
Publication statusPublished - 2012
Externally publishedYes

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