OFFSET
1,2
COMMENTS
Coulomb self-energy of a system of electric charges is the total electrostatic potential energy of interaction between charge elements.
For a uniformly charged two-dimensional square with a total charge Q and a side length L it is equal to c * k*Q^2/L, where k is the Coulomb constant (A182999) and c is this constant.
LINKS
Orion Ciftja, Coulomb self-energy and electrostatic potential of a uniformly charged square in two dimensions, Physics Letters A, Vol. 374, No. 7 (2010), pp. 981-983, alternative link.
Wikipedia, Electric potential energy.
FORMULA
Equals 2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)).
EXAMPLE
1.486604799123689351264092833819785899009872739605305...
MATHEMATICA
RealDigits[2*(1 - Sqrt[2])/3 + 2*Log[1 + Sqrt[2]], 10, 100][[1]]
PROG
(PARI) 2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)) \\ Michel Marcus, Jul 15 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jul 15 2020
STATUS
approved