Dyonic solutions of Maxwell field equations in arbitrary media
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ORIGINAL PAPER
Dyonic solutions of Maxwell field equations in arbitrary media I Joshi* and J S Garia Department of Physics, L. S. M. Govt. Post Graduate College, Pithoragarh, Uttarakhand, India Received: 13 December 2018 / Accepted: 29 August 2019
Abstract: In this paper, we report the reformulation of Maxwell equations for dyon in arbitrary media and it’s role in order to obtain the three set of solutions in terms of charge density q, current density J, polarization P, and magnetization M. Present study determines the electric field E, electric displacement vector D, magnetic induction vector H, and magnetic field B as integrals of retarded charge density q, current density J, polarization P and magnetization M, and their retarded spatial and temporal derivatives. Keywords: Dyon; Monopole; Polarization; Magnetization PACS Nos.: 14.80Hv
1. Introduction The study seeks to develop an understanding of Maxwell equations in arbitrary media in the situation of simultaneously containing electric and magnetic charge (dyon). Dirac introduced the possible existence of magnetic charge (monopole) and established the corresponding Maxwell field equations between the basic magnetic charge g and the elementary electric charge e in the famous Dirac quantization condition, i.e., eg ¼ n h2c [1, 2]. Generalizing Dirac quantization condition, Schwinger provided the quantization condition for dyons as a candidate for Quarks models [3, 4]: e1 g2 e2 g1 ¼ 2pn
ð1Þ
For the experimental verification of magnetic monopole, many attempts were made [5, 6] and several theoretical problems were solved by the invention of dyon carrying simultaneous existence of electric and magnetic charge [7–10]. Research into the field of monoploles got a tremendous boost after the work of t’ Hooft [11] and Polyakov [12] and its extension by Julia and Zee [13]. Now these particles became an intrinsic part of all current grand unified theories (GUT) with their large importance in connection with various physical problems [14–22]. In this paper, we report the reformulation of Maxwell equations for dyon in arbitrary media and it’s role in order to
obtain the two set of solutions in terms of charge density q, current density J, polarization P, and magnetization M. Maxwell equations in the empty space [23] (the vacuum) are already well known and have been reconstructed for the existence of matter with electric and magnetic charges. Motivated by the work of Jefimenko [24], who derived the solution of the Maxwell equation in arbitrary media (dielectric and magnetic) in the absence of monopole, we report the extended solution of Maxwell equations for dyon in arbitrary media (dielectric and magnetic media). The first set of the solutions expresses the fields E, H, and B in terms of retarded charge density q, retarded current density J, retarded polarization P, retarded magnetization M, and retarded spatial and temporal derivatives of q, J, P and M. The second set contains no spatial derivatives where the solutions have imposed no restrictions on any of the quanti
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