任意五边形均匀带电线框的空间电势和空间电场

摘要

The electric potential distribution expression for uniformly charged wire at arbitrarily space position is derived from the expression of electric potential distribution for uniformly charged wire.Then,the electric field intensity coordinate component expression for uniformly charged wire at arbitrarily space position is deduced from the relation between electric potential gradient and electric field.Taken these expressions as examples,the electric potential and electric field intensity for the arbitrarily pentagon charged coil are calculated,and the special cases for uniformly equilateral pentagon charged coil are discussed.By introducing each vertex coordinates into the above expression accordingly,the electric potential and electric field for any arbitrary polygon charge wire can be calculated in principle.Therefore,the method presented in this paper has good universality.In addition,the results of electric potential and electric field distribution obtained are the functions of spatial coordinates,which can be conveniently applied in engineering technology.%从均匀带电直线的电势表达式出发,给出了其在xy平面内任意空间位置时的电势表达式.利用电场强度与电势梯度的关系,进而导出了其在xy平面内任意位置时场强的坐标分量表达式.利用上述表达式,作为实例,我们对均匀带电任意五边形线框的空间电势和空间电场进行了计算,并讨论了正五边形的特殊情况.只需将顶点坐标代入相应的表达式,原则上可以计算任意多边形均匀带电线框的电势和电场,因此,所采用的方法具有普适性.同时,所得到的电势分布和电场分布都是空间坐标的函数,便于在工程技术中应用.