A336274 Decimal expansion of the dimensionless coefficient of the Coulomb self-energy of a uniformly charged three-dimensional cube.

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

Offset: 0

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 three-dimensional cube with a total charge Q and an edge length L it is equal to c * k*Q^2/L, where k is the Coulomb constant (A182999) and c is this constant.

Examples

			0.94115632219483008005280041943418379392623144015535...
		

Links

• Orion Ciftja, Coulomb self-energy of a uniformly charged three-dimensional cube, Physics Letters A, Vol. 375, No. 3 (2011), pp. 766-767, alternative link.
• Wikipedia, Electric potential energy.

Crossrefs

Cf. A085469, A182999, A336275.

Programs

Mathematica

RealDigits[(1 + Sqrt[2] - 2*Sqrt[3])/5 - Pi/3 + Log[(1 + Sqrt[2])*(2 + Sqrt[3])], 10, 100][[1]]

PARI

(1 + sqrt(2) - 2*sqrt(3))/5 - Pi/3 + log((1+sqrt(2))*(2+sqrt(3))) \\ Michel Marcus, Jul 15 2020

Formula

Equals (1 + sqrt(2) - 2*sqrt(3))/5 - Pi/3 + log((1 + sqrt(2)) * (2 + sqrt(3))).