平面载流线圈在匀强磁场中所受的磁力矩

平面载流线圈在匀强磁场中所受到的磁力矩是电磁学和电动力学中重要问题之一 ,其数学表达式多数是以载流矩形线圈放在均匀磁场中而且转轴和磁力线垂直为特例推导出来的 ,推导过程和结论均有一定局限性。通过安培定律和力矩的定义式以及斯托克斯定理推导出任意形状载流线圈在匀强磁场中处在不同方位时 ,分别对质心参考点和质心轴以及固定转轴的磁力矩的数学表达式。推导方法不仅准确 ,而且从推导过程中可以看出其数学表达式适用于计算任意形状的平面载流线圈在匀强磁场中所受到的磁力矩 ,具有更普遍的意义

The Moment of Magnetic Force of Plane Current-Carrying Coil That is Accepted in Uniform Magnetic Field

It is one of important problem that moment of magnetic force of planary current-carrying coil is accepted in uniform field. The mathematical formula of moment of magnetic force is deduced according to a current-carrying rectangular whose axis is perpendicular to a uniform magnetic field as a special example. The deducing process and conclusion have a certain limitation. In the paper, the mathematical formulas of magnetic force moment of mass center being as referencing point, of mass center axis, of fixed axis on a current-carrying arbitrary shape planary loop that is oriented arbitrarily in uniform field are deduced respectively according to Ampere's law and the definition of moment of force as well as Stoke's theorem. The defucing process is accurate and it is given that the mathematical formulas of moment of magnetic force can be applied to calculate the moment of magnetic force on arbitrary shape planary current-carrying coil. Therefore, it is of more general significance.