A336275 Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged two-dimensional square.

1, 4, 8, 6, 6, 0, 4, 7, 9, 9, 1, 2, 3, 6, 8, 9, 3, 5, 1, 2, 6, 4, 0, 9, 2, 8, 3, 3, 8, 1, 9, 7, 8, 5, 8, 9, 9, 0, 0, 9, 8, 7, 2, 7, 3, 9, 6, 0, 5, 3, 0, 5, 4, 3, 9, 3, 8, 8, 8, 0, 4, 7, 2, 5, 3, 1, 2, 9, 3, 2, 7, 1, 6, 1, 3, 5, 9, 8, 0, 8, 1, 6, 4, 3, 3, 8, 2

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

Table of n, a(n) for n=1..87.

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

Cf. A085469, A182999, A336274.

Sequence in context: A243376 A200411 A198885 * A177157 A081573 A201527

Adjacent sequences: A336272 A336273 A336274 * A336276 A336277 A336278

Keyword

nonn,cons

Author

Amiram Eldar, Jul 15 2020

Status

approved