在经典Maxwell方程组的基础上,利用四维空间矢量和四维电磁场张量的变化规律,将Maxwell方程组Lorentz表述的场方程组变换成四维张量形式,证明了Lorentz表述四维张量形式的特点,验证了Maxwell方程组的协变性以及Lorentz表述的四维张量形式的对称性,从而更好地解释了电磁场的运动规律。通过列举实际算例验证了本文算法的实用性和有效性,简化了运动介质相关的问题,体现了在解决运动介质方面问题的优越性,为运动问题的解决提供了一定的帮助。
Abstract
In this paper, we transform the Lorentz expression of Maxwell’s equations to a four-dimensional tensor form by defining vector potential, scalar potential, the four-dimensional space vector and the electromagnetic field tensor. The result can better explain the movement of the electromagnetic field and verify the invariance of Maxwell’s equations and the symmetry of the Lorentz expression of the four-dimensional tensor form. By listing actual examples we can verify the usefulness and effectiveness of the arithmetical method. At the same time, it can simplify the problem of a moving medium and provide some assistance in solving the movement problem, which demonstrates its superiority over the traditional form.
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1]肖志俊. 对麦克斯韦方程组的探讨[J]. 通信技术, 2008, 41(9): 81-83.
Xiao Z J. The discussion of Maxwell’s equations[J]. Communications Technology, 2008, 41(9): 81-83. (in Chinese)
[2]陈俊华. 关于麦克斯韦方程组的讨论[J]. 物理与工程, 2002, 12(4): 18-20.
Chen J H. The argumentation about Maxwell’s equations[J]. Physics and Engineering, 2002, 12(4): 18-20. (in Chinese)
[3]郭硕鸿. 电动力学[M]. 2版. 北京: 人民教育出版社, 1997.
Guo S H. Electrodynamics [M]. 2nd Ed. Beijing: People’s Education Press, 1997. (in Chinese)
[4]鲍亦兴. 变形连续介质中的电磁力[M]. 北京: 科学出版社, 1996.
Bao Y X. The electromagnetic force of deformation and continuum[M]. Beijing: Science Press, 1996. (in Chinese)
[5]李廉林, 李芳. 基于Laguerre多项式及PML边界的时域Maxwell方程解[J]. 信息科学, 2008, 38(8): 1331-1338.
Li L L, Li F. The timedomain Maxwell equations based on Laguerre polynomial and PML boundary[J]. Information Sciences, 2008, 38(8): 1331-1338. (in Chinese)
[6]Sun Y, Tse P S P. Symplectic and multisymplecticnumerical methods for Maxwell’s equations[J]. Journal of Computational Physics, 2011, 230: 2076-2094.
[7]Kou Y L, Ding S J. Partial compactness for landau-lifshitz maxwell equation in twodimension[J]. Acta Mathematica Scientia, 2011, 31B(2): 727-748.
[8]张祥雪, 程艳霞, 范秀华, 等. 洛伦兹力可看作静止电荷所受电场力的相对论效应[J]. 物理与工程, 2006, 16(4): 26-28.
Zhang X X, Cheng Y X, Fan X H, et al. The relativistic effects that Lorentz force can be seen as electric force of electric charge[J]. Physics and Engineering, 2006, 16(4): 26-28. (in Chinese)
[9]Cohen G, Ferrieres X, Pernet S. Discontinuous Galerkin methods for Maxwell’s equations in the time domain[J]. Comptes Rendus Physique, 2006, 7: 494-500.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}