Recent interest in problems in higher space di mensions is becoming increasingly important and attracted the attention of many investigators in variety of fields in physics. In this paper, the electrostatic energy of two geometries (a charged spherical shell and a nonconducting sphere) is calculated in higher space dimension, N. It is shown that as the space dimension increases, up to N = 9, the electrostatic energy of the two geometries decreases and beyond N = 9 it increases. Furthermore, we discuss a simple example which illustrates classical renormalization in electrostatics in higher dimensions.
Brack, M. and Murthy, M.V. (2003) Harmonically trapp ed fermion gases: Exact and asymptotic results in arbitrary dimensions. Journal of Physics A: Mathematical and General, 36(4), 11111133.
Weldon, H.A. (2003) Quantization of higherderivative field theories. Annals of Physics, 305(2), 137150.
Kajimoto, N., Manaka, T. and Iwamoto, M. (2006) Electrostatic energies stored in dipolar films and analysis of decaying process of a large surface potential of ALq3 films. Chemical Physics Letters, 430(46), 340344.