OFFSET
0,3
COMMENTS
Lampard dealt in a paper, see the links, with the calculation of internal cross capacitances of cylinders under certain conditions of symmetry. Van der Pauw generalized Lampard's results with the formula exp(-4*Pi^2*Cab,cd) + exp(-4*Pi^2*Cbc,da) = 1, see the links. Van der Pauw observed that in Lampard's case of symmetry, the two capacitances Cab,cd and Cbc,da are mutually equal, and hence are both equal to C = log(2)/(4*Pi^2) independently of the size or shape of the cross-section, which is Lampard's theorem.
Lampard's constant is closely related to Van der Pauw's constant A163973.
This constant was named after the Australian professor of electrical engineering Douglas Geoffrey Lampard (1927 - 1994). - Amiram Eldar, Dec 03 2020
LINKS
D. G. Lampard, A new theorem in electrostatics with applications to calculable standards of capacitance, Proceedings of the IEE, Vol. 104, No. 6, pp. 271-280, September 1957.
L. J. van der Pauw, A method of measuring specific resistivity and Hall effect of disc of arbitrary shape, Philips Research Reports, Vol. 13. no. 1, pp 1-9, February 1958.
FORMULA
C = log(2)/(4*Pi^2).
EXAMPLE
0.0175576231931707191...
PROG
(PARI) log(2)/(4*Pi^2) \\ Michel Marcus, Jul 04 2015
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Johannes W. Meijer, Jul 03 2015
STATUS
approved