Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(3): 030301    DOI: 10.1088/1674-1056/22/3/030301
GENERAL Prev   Next  

Complex Maxwell's equations

A. I. Arbab
Department of Physics, Faculty of Science, University of Khartoum, Khartoum 11115, Sudan
Abstract  A unified complex model of Maxwell's equations is presented. The wave nature of electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities. A new vacuum solution is obtained. A new transformation under which Maxwell's equations are invariant is proposed. This transformation extends the ordinary gauge transformation to include charge-current besides scalar-vector potential. An electric dipole moment is found to be related to magnetic charges. The Dirac's quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges. We generalize Maxwell's equations to include longitudinal waves. A formal analogy between this formulation and Dirac's equation is discussed.
Keywords:  Maxwell's equations      duality transformations      magnetic charge (monopole)  
Received:  24 August 2012      Revised:  28 September 2012      Accepted manuscript online: 
PACS:  03.50.De (Classical electromagnetism, Maxwell equations)  
  04.20.Jb (Exact solutions)  
Corresponding Authors:  A. I. Arbab     E-mail:  aiarbab@uofk.edu

Cite this article: 

A. I. Arbab Complex Maxwell's equations 2013 Chin. Phys. B 22 030301

[1] Jackson J D 1962 Classical Electrodynamics (John Wiley & Sons Inc.)
[2] Arbab A I 2009 Prog. Phys. 2 8
[3] Silberstein L 1907 Ann. der Physik 24 783
[4] Abreu E M C and Hott M B 2000 Phys. Rev. D 62 027702
[5] Vachaspati 1960 Proc. Nat. Inst. Sci. India 26 359
[6] Whittaker E T 1904 Proc. Lond. Math. Soc. 1 367
[7] Proca A 1936 J. Phys. Radium. 7 347
[8] Bialynicki-Birula I and Bialynicka-Birula Z 2006 Opt. Commun. 264 342
[9] Arbab A I and Yassein F A 2012 J. Mod. Phys. 3 163
[10] Arbab A I and Yassein F A 2010 J. Electrom. Anal. Appl. 2 457
[11] Arbab A I and Widatallah H M 2010 Chin. Phys. Lett. 27 084703
[12] Aharonov Y and Bohm D 1959 Phys. Rev. 115 485
[13] t'Hooft G and Nobbenhuis S 2006 Class. Quantum Grav. 23 3819
[14] Arbab A I and Widatallah H M 2010 Europhys. Lett. 92 23002
[15] Dirac P A M 1931 Proc. R. Soc. A 133 60
[16] Kang L I, Chen W and Naon C M 2003 Chin. Phys. Lett. 20 321
[17] Khomskii D I 2012 Nature Commun. 3 904
[18] Ji A C, Xie X C and Liu W M 2007 Phys. Rev. Lett. 99 183602
[19] Abliz A, Gao H J, Xie X C, Wu Y S and Liu W M 2006 Phys. Rev. A 74 052105
[20] Bjorken J D and Drell S 1964 Relativistic Quantum Mechanics (New York: McGraw-Hill)
[1] Bidirectional visible light absorber based on nanodisk arrays
Qi Wang(王琦), Fei-Fan Zhu(朱非凡), Rui Li(李瑞), Shi-Jie Zhang(张世杰), and Da-Wei Zhang(张大伟). Chin. Phys. B, 2023, 32(3): 030205.
[2] Ultra-broadband absorber based on cascaded nanodisk arrays
Qi Wang(王琦), Rui Li(李瑞), Xu-Feng Gao(高旭峰), Shi-Jie Zhang(张世杰), Rui-Jin Hong(洪瑞金), Bang-Lian Xu(徐邦联), and Da-Wei Zhang(张大伟). Chin. Phys. B, 2022, 31(4): 040203.
[3] Discrete wavelet structure and discrete energy of classical plane light waves
Xing-Chu Zhang(张兴初) and Wei-Long She(佘卫龙). Chin. Phys. B, 2021, 30(4): 040301.
[4] Propagation characteristics of oblique incidence terahertz wave through non-uniform plasma
Antao Chen(陈安涛), Haoyu Sun(孙浩宇), Yiping Han(韩一平), Jiajie Wang(汪加洁), Zhiwei Cui(崔志伟). Chin. Phys. B, 2019, 28(1): 014201.
[5] General series expression of eddy-current impedance for coil placed above multi-layer plate conductor
Yin-Zhao Lei(雷银照). Chin. Phys. B, 2018, 27(6): 060308.
[6] Analytical model of tilted driver-pickup coils for eddy current nondestructive evaluation
Bing-Hua Cao(曹丙花), Chao Li(李超), Meng-Bao Fan(范孟豹), Bo Ye(叶波), Gui-Yun Tian(田贵云). Chin. Phys. B, 2018, 27(3): 030301.
[7] Physical interpretation of Planck's constant based on the Maxwell theory
Donald C Chang(张东才). Chin. Phys. B, 2017, 26(4): 040301.
[8] Binding energy of the donor impurities in GaAs-Ga1-xAlxAs quantum well wires with Morse potential in the presence of electric and magnetic fields
Esra Aciksoz, Orhan Bayrak, Asim Soylu. Chin. Phys. B, 2016, 25(10): 100302.
[9] Inverse problem of pulsed eddy current field of ferromagnetic plates
Chen Xing-Le (陈兴乐), Lei Yin-Zhao (雷银照). Chin. Phys. B, 2015, 24(3): 030301.
[10] Erratum:Classical interpretations of relativistic precessions
Sankar Hajra. Chin. Phys. B, 2014, 23(9): 090401.
[11] Complete eigenmode analysis of a ladder-type multiple-gap resonant cavity
Zhang Chang-Qing (张长青), Ruan Cun-Jun (阮存军), Zhao Ding (赵鼎), Wang Shu-Zhong (王树忠), Yang Xiu-Dong (杨修东). Chin. Phys. B, 2014, 23(8): 088401.
[12] Characteristics of spectral-hole burning in Tm3+:YAG based on the perturbation theory
Zhang Shi-Yu (张世宇), Ma Xiu-Rong (马秀荣), Zhang Shuang-Gen (张双根), Chen-Lei (陈雷), Wang Xia-Yang (王夏洋), Mu Kuan-Lin (穆宽林), Wang Song (王松). Chin. Phys. B, 2014, 23(6): 060304.
[13] Classical interpretations of relativistic precessions
Sankar Hajra. Chin. Phys. B, 2014, 23(4): 040402.
[14] The propagation of shape changing soliton in a nonuniform nonlocal media
L. Kavitha, C. Lavanya, S. Dhamayanthi, N. Akila, D. Gopi. Chin. Phys. B, 2013, 22(8): 084209.
[15] Prediction and experimental measurement of electromagnetic thrust generated by a microwave thruster system
Yang Juan (杨涓), Wang Yu-Quan (王与权), Ma Yan-Jie (马艳杰), Li Peng-Fei (李鹏飞), Yang Le (杨乐), Wang Yang (王阳), He Guo-Qiang (何国强). Chin. Phys. B, 2013, 22(5): 050301.
No Suggested Reading articles found!