变速旋转带电体的磁偶极辐射阻尼力矩公式与算例
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摘要
通过电磁场矢势的远场多极矩展开理论,引入旋转带电体的一个本体电矩张量以计算其磁矩,推导了定轴变角速转动带电体的磁偶极辐射功率及其受到的辐射阻尼力矩公式。研究表明,忽略延迟效应,在非相对论远场情形以及准周期平均意义下,变速旋转带电体的辐射阻尼力矩与其角速度的四阶导数有关;给出了若干特殊形状变速旋转带电体的磁距、磁偶极辐射功率和辐射阻尼力矩的具体算例;另外,以带电简谐转子为例,利用微扰法讨论了辐射阻尼力矩对其转动的影响。
Deriving from the multipole-moment and far-field expansion theory of the electromagnetic vector potential,an electric quadrupole moment tensor was introduced to calculate the magnetic moment of a rotational charged body.And its magnetic-dipole radiation power was concretely derived,subsequently,the radiation damping torque upon the rotational charged body about a fixed axis was also deduced.The research results show that,if the retarded effect is ignored,the radiation damping torque is generated from the fourth-order derivative of the angular speed with respect to time,under the non-relativistic far-field case,and on average in a quasi-periodic process.Some calculated examples of magnetic moment,magnetic-dipole radiation power and the radiation damping torque,for several concrete charged bodies of special shape,were numerated and listed in a table.Moreover,a concrete rotational vibrator in a simple harmonic oscillation was taken as a reference to illustrate the general radiation theory.By means of perturbation method,the influence of the damping torque upon the rotational vibrator was also discussed in detail.
Deriving from the multipole-moment and far-field expansion theory of the electromagnetic vector potential,an electric quadrupole moment tensor was introduced to calculate the magnetic moment of a rotational charged body.And its magnetic-dipole radiation power was concretely derived,subsequently,the radiation damping torque upon the rotational charged body about a fixed axis was also deduced.The research results show that,if the retarded effect is ignored,the radiation damping torque is generated from the fourth-order derivative of the angular speed with respect to time,under the non-relativistic far-field case,and on average in a quasi-periodic process.Some calculated examples of magnetic moment,magnetic-dipole radiation power and the radiation damping torque,for several concrete charged bodies of special shape,were numerated and listed in a table.Moreover,a concrete rotational vibrator in a simple harmonic oscillation was taken as a reference to illustrate the general radiation theory.By means of perturbation method,the influence of the damping torque upon the rotational vibrator was also discussed in detail.
引文
[1]虞国寅,周国全.电动力学[M].武汉:武汉大学出版社,2008:87-88.YU G Y,ZHOU G Q.Electrodynamics[M].Wuhan:Wuhan University Press,2008:87-88(Ch).
[2] ZHOU G Q.Charge moment tensor and the magnetic moment of rotational charged bodies[J].Progress in Electromagnetics Research,2007,68:156-160.DOI:10.2528/PIER06080603.
[3]周国全.一个新的电矩张量及其在电磁场中的应用[M].萨尔布吕肯:金琅学术出版社,2015:11-25.ZHOU G Q.A New Charge Moment Tensor and Its Application to Electromagnetism[M].Saarbrucken:Golden Light Academic Publishing,2015:11-25(Ch).
[4]周国全.电矩张量与旋转带电体的磁矩[J].大学物理,2007,26(4):7-11.DOI:10.16854/j.cnki.1000-0712.2007.04.005.ZHOU G Q.Charge moment tensor and the magnetic moment of a rotating charged body[J].College Physics,2007,26(4):7-11.DOI:10.16854/j.cnki.1000-0712.2007.04.005(Ch).
[5] ZHOU G Q,ZHOU W J.The magnetic-moment quadric and conditions of vanishing magnetic moment for a rotational charged body[J].Progress in Electromagnetics Research,2007,70:211-223.DOI:10.2528/PIER07011201.
[6]徐定藩,吕正山.带电体定轴转动的磁矩计算[J].大学物理,1997,16(4):3-4.DOI:10.16854/j.cnki.1000-0712.1997.04.002.XU D F,LZ S.The calculation of magnetic moment of an electrified body rotating about a fixed-axis[J].College Physics,1997,16(4):3-4.DOI:10.16854/j.cnki.1000-0712.1997.04.002(Ch).
[7]周国全.旋转带电体磁矩计算的若干法则与算例[J].物理与工程,2004,14(2):16-19.DOI:10.3969/j.issn.1009-7104.2004.02.005.ZHOU G Q.Principles and examples about calculating the magnetic moment of charged rotational bodies[J].Physics and Engineering,2004,14(2):16-19.DOI:10.3969/j.issn.1009-7104.2004.02.005(Ch).
[8]周国全.旋转带电体磁矩的推广的平行轴定理[J].大学物理,2016,35(11):9-12.DOI:10.16854/j.cnki.1000-0712.2016.0157.ZHOU G Q.The generalized parallel-axes theorem for the magnetic moment of a rotational charged body[J].College Physics,2016,35(11):9-12.DOI:10.16854/j.cnki.1000-0712.2016.0157(Ch).
[9] ZHOU G Q.Several rules about the magnetic moment of rotational charged bodies[J].Progress in Electromagnetics Research Symposium,2007,3(6):812-816.
[10]ZHOU G Q,GUAN C.Charge moment tensor and its application to a rotational charged rigid body in a uniform magnetic field[J].Journal of Electromagnetic Waves and Applications,2008,22(16):2179-2190.
[11]周国全,张斯磊,肖霄.带电电介质刚体在匀强磁场中的转动动力学方程[J].武汉大学学报(理学版),2009,55(2):187-190.DOI:10.14188/j.1671-8836.2009.02.014.ZHOU G Q,ZHANG S L,XIAO X.Dynamical theory of rotational charged rigid body in an uniform magnetic field[J].Journal of Wuhan University(Natural Science Edition),2009,55(2):187-190.DOI:10.14188/j.1671-8836.2009.02.014(Ch).
[12]侯舜华.辐射阻尼对带电粒子运动的影响[J].大学物理,1996,15(5):7-11.DOI:10.16854/j.cnki.1000-0712.1996.05.003.HOU S H.Effects of the radiation damping on the motion of charged particles[J].College Physics,1996,15(5):7-11.DOI:10.16854/j.cnki.1000-0712.1996.05.003(Ch).
[13]刘觉平.电动力学[M].北京:高等教育出版社,2004:359-360.LIU J P.Electrodynamics[M].Beijing:Higher Education Press,2004:359-360(Ch).
[14]郭硕鸿.电动力学[M].北京:高等教育出版社,2008:200-205,260-262.GUO S H.Electrodynamics[M].Beijing:Higher Education Press,2008:200-205,260-262(Ch).
[15]周国全.一个矢量定理及其在物理教学与研究中的应用[J].物理通报,2015(6):32-35.DOI:10.3969/j.issn.0509-4038.2015.06.010.ZHOU G Q.A vector theorem and its application in physics teaching and research[J].Physics Bulletin,2015(6):32-35.DOI:10.3969/j.issn.0509-4038.2015.06.010(Ch).
[2] ZHOU G Q.Charge moment tensor and the magnetic moment of rotational charged bodies[J].Progress in Electromagnetics Research,2007,68:156-160.DOI:10.2528/PIER06080603.
[3]周国全.一个新的电矩张量及其在电磁场中的应用[M].萨尔布吕肯:金琅学术出版社,2015:11-25.ZHOU G Q.A New Charge Moment Tensor and Its Application to Electromagnetism[M].Saarbrucken:Golden Light Academic Publishing,2015:11-25(Ch).
[4]周国全.电矩张量与旋转带电体的磁矩[J].大学物理,2007,26(4):7-11.DOI:10.16854/j.cnki.1000-0712.2007.04.005.ZHOU G Q.Charge moment tensor and the magnetic moment of a rotating charged body[J].College Physics,2007,26(4):7-11.DOI:10.16854/j.cnki.1000-0712.2007.04.005(Ch).
[5] ZHOU G Q,ZHOU W J.The magnetic-moment quadric and conditions of vanishing magnetic moment for a rotational charged body[J].Progress in Electromagnetics Research,2007,70:211-223.DOI:10.2528/PIER07011201.
[6]徐定藩,吕正山.带电体定轴转动的磁矩计算[J].大学物理,1997,16(4):3-4.DOI:10.16854/j.cnki.1000-0712.1997.04.002.XU D F,LZ S.The calculation of magnetic moment of an electrified body rotating about a fixed-axis[J].College Physics,1997,16(4):3-4.DOI:10.16854/j.cnki.1000-0712.1997.04.002(Ch).
[7]周国全.旋转带电体磁矩计算的若干法则与算例[J].物理与工程,2004,14(2):16-19.DOI:10.3969/j.issn.1009-7104.2004.02.005.ZHOU G Q.Principles and examples about calculating the magnetic moment of charged rotational bodies[J].Physics and Engineering,2004,14(2):16-19.DOI:10.3969/j.issn.1009-7104.2004.02.005(Ch).
[8]周国全.旋转带电体磁矩的推广的平行轴定理[J].大学物理,2016,35(11):9-12.DOI:10.16854/j.cnki.1000-0712.2016.0157.ZHOU G Q.The generalized parallel-axes theorem for the magnetic moment of a rotational charged body[J].College Physics,2016,35(11):9-12.DOI:10.16854/j.cnki.1000-0712.2016.0157(Ch).
[9] ZHOU G Q.Several rules about the magnetic moment of rotational charged bodies[J].Progress in Electromagnetics Research Symposium,2007,3(6):812-816.
[10]ZHOU G Q,GUAN C.Charge moment tensor and its application to a rotational charged rigid body in a uniform magnetic field[J].Journal of Electromagnetic Waves and Applications,2008,22(16):2179-2190.
[11]周国全,张斯磊,肖霄.带电电介质刚体在匀强磁场中的转动动力学方程[J].武汉大学学报(理学版),2009,55(2):187-190.DOI:10.14188/j.1671-8836.2009.02.014.ZHOU G Q,ZHANG S L,XIAO X.Dynamical theory of rotational charged rigid body in an uniform magnetic field[J].Journal of Wuhan University(Natural Science Edition),2009,55(2):187-190.DOI:10.14188/j.1671-8836.2009.02.014(Ch).
[12]侯舜华.辐射阻尼对带电粒子运动的影响[J].大学物理,1996,15(5):7-11.DOI:10.16854/j.cnki.1000-0712.1996.05.003.HOU S H.Effects of the radiation damping on the motion of charged particles[J].College Physics,1996,15(5):7-11.DOI:10.16854/j.cnki.1000-0712.1996.05.003(Ch).
[13]刘觉平.电动力学[M].北京:高等教育出版社,2004:359-360.LIU J P.Electrodynamics[M].Beijing:Higher Education Press,2004:359-360(Ch).
[14]郭硕鸿.电动力学[M].北京:高等教育出版社,2008:200-205,260-262.GUO S H.Electrodynamics[M].Beijing:Higher Education Press,2008:200-205,260-262(Ch).
[15]周国全.一个矢量定理及其在物理教学与研究中的应用[J].物理通报,2015(6):32-35.DOI:10.3969/j.issn.0509-4038.2015.06.010.ZHOU G Q.A vector theorem and its application in physics teaching and research[J].Physics Bulletin,2015(6):32-35.DOI:10.3969/j.issn.0509-4038.2015.06.010(Ch).