Abstract
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.
Highlights
The space dimension N plays an important role in studying many physical problems
A connected technique to electrostatic energy is the renormalization in classical field theory
In the present paper, we will consider an example of classical renormalization of electrostatic energy in higher space dimensions
Summary
The space dimension N plays an important role in studying many physical problems. It has been used for the radial wave functions of the hydrogen like atoms in N dimensions [1,2]. A connected technique to electrostatic energy is the renormalization in classical field theory. Corbò [16] considered renormalization technique in classical fields and Tort [17] discussed renormalization of electrostatic energy. In the present paper, we will consider an example of classical renormalization of electrostatic energy in higher space dimensions. The organization of the present paper is as follows: In Section 2, we consider electrostatic energy in a hyper spherical shell.
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