基于张量方法探究导体球在线性梯度磁场中的运动  

Exploration of the motion of conduct sphere in a linear gradient magnetic field by the tensors method

作　　者：沈航正 蔡卓凡 陶小平[1] 赵伟[1] 浦其荣[1] 赵霞[1] 张增明[1] SHEN Hang-zheng;CAI Zhuo-fan;TAO Xiao-ping;ZHAO Wei;PU Qi-rong;ZHAO Xia;ZHANG Zeng-ming(School of Physical Sciences,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]中国科学技术大学物理学院,安徽合肥230026

出　　处：《大学物理》2025年第1期106-111,共6页College Physics

摘　　要：2023年大学生物理学术竞赛(以下文本中均简称为CUPT)中的第二题振荡球(Oscillating sphere)要求研究一个表面导电的导体球在磁场中的运动.本文从麦克斯韦方程组出发,基于良导体的性质,利用级数展开和分离变量法,将问题转化为定边界的泊松方程,再利用张量表述下的球谐函数,研究了非铁磁导体球壳在均匀磁场和线性梯度磁场中受到的力和力矩,获得了完备的描述导体球壳在线性梯度场中运动模式的微分方程,求解并设计实验探究了动力学方程的若干特解,在大学物理实验条件下,证明了导体球模型平动与转动的衰减以及相互的耦合运动规律.The second question in the 2023 China Undergraduate Physics Tournament(CUPT)“Oscillating sphere”requires the study of the motion of a surface conductive sphere in a magnetic field.Starting from the Maxwell equation system and based on the properties of good conductors,this article uses series expansion and separation of variables method to transform the problem into a Poisson equation with fixed boundaries.Then,using the spherical harmonic function under tensor expression,the force and torque of a non ferromagnetic conductive spherical shell in a uniform magnetic field and a linear gradient magnetic field are studied,and a complete differential equation describing the motion mode of the conductor spherical shell in a linear gradient field is obtained,We solved and designed experiments to explore several special solutions of the dynamic equation.Under the conditions of university physics experiments,we demonstrated the attenuation of the translational and rotational motion of the conductor ball model,as well as the coupling motion between them.

关 键 词：CUPT IYPT 磁场 球谐函数 

分 类 号：O441.3[理学—电磁学]