Open AccessII. The potential of an anchor ring
Publication year - 1893
Publication title -
philosophical transactions of the royal society of london. a
Language(s) - English
Resource type - Journals
eISSN - 2053-9231
pISSN - 0264-3820
DOI - 10.1098/rsta.1893.0002
Subject(s) - ring (chemistry) , radius , infinity , mathematics , point (geometry) , laplace's equation , mathematical analysis , set (abstract data type) , combinatorics , physics , geometry , pure mathematics , computer science , differential equation , chemistry , computer security , organic chemistry , programming language
In this Paper I have developed a method of dealing with questions connected with Anchor Rings. Ifr, θ, ϕ be the coordinates of any point outside an anchor ring, whose central circle is of radiusc , then ∫π 0 dϕ/√(r2 +c2 - 2cr sinθ cosϕ )is a solution of Laplace’s equation, finite at all external points and vanishing at infinity. Let this be called I. ThendI/dz is another solution; and two sets of solutions may be found by differentiating I andd I/d z any number of times with respect toc . These solutions are symmetrical with respect to the axis of the ring. In the first setz is involved only in even powers; in the second set in odd powers.