旋转带电体的磁矩二次曲面及其零磁矩条件

Magnetic Moment Quadric of Rotational Charged Body and Its Condition of Zero Magnetic Moment

基于带电体的一个不同于电四极矩的电矩张量的性质,引入了标量电矩二次曲面及电矩主轴的概念,根据标量电矩与旋转带电体的磁矩之间的线性关系,运用二次曲面的解析理论,得到了旋转带电体的磁矩二次曲面分布律的分类判别关系式,推导出任意旋转带电体的零磁矩条件.理论分析的结果表明在磁矩二次曲面中任意一条通过原点O的渐近线都代表着一个导致零磁矩的转轴方向.

Based on the property of the electrical moment tensor （which is different from the existent electric multiple moment） of a charged body, new concepts such as principal axes, principal-axis scalar charge moment and charge moment quadric are proposed in this paper. According to the linear relationship between the scalar charge moment and the magnetic moment of a rotational charged body, by means of analytic spatial geometry, the criterion formulae determining the correspondence relationship between quadric distributive laws of magnetic moment and the parameters of tensor T are obtained and classified in detail in a table. The condition of zero magnetic moment for an arbitrary rotational body with given charge distribution has been derived. We conclude that any rotation axis which passes through origin O and along with any asymptotic line of the quadric （hyperboloids or hyperbolic cylinders, etc. ） can lead to a vanishing magnetic moment.