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

Author

Amiram Eldar, Jul 15 2020

Keywords

• nonn
• cons

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.

Examples

			1.486604799123689351264092833819785899009872739605305...
		

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.

Crossrefs

Cf. A085469, A182999, A336274.

Programs

Mathematica

RealDigits[2*(1 - Sqrt[2])/3 + 2*Log[1 + Sqrt[2]], 10, 100][[1]]

PARI

2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)) \\ Michel Marcus, Jul 15 2020

Formula

Equals 2*(1 - sqrt(2))/3 + 2 * log(1 + sqrt(2)).