共轴平行圆盘的电容系数

CAPACITY COEFFICIENTS OF COAXIAL PARALLEL DISK

由泊松方程和边界条件,给出了共轴平行不同大小圆盘的电势含两个待定函数的积分表达式.电势在圆盘上为定值,电场在圆盘外所在平面上连续,由此得到两个待定函数的偶合积分方程.利用数值积分中的Gauss-Lobatto公式,得到了圆盘上电荷数值表达式.两个圆盘上的电荷与圆盘电势成线性关系,其系数矩阵为电容系数矩阵.给出了电容系数和圆盘半径与圆盘间距比值得等高线图.

From Poisson equation and boundary condition, the electric potential of two differ- ent coaxial parallel disks is derived, which is an integral expression with two undefined functions. Because the electric potential is constant on the disk and the electric field is continuous on the plane outside the two disks, two coupled integrated equations of the undefined func- tions can be obtained from the boundary conditions. The numerical expression of charges on the disks are got by Gauss-Lobatto method. Relationship between charges and electric poten- tial on two discs are shown to be linear, and the coefficients matrix between the charges and the potentials are defined as capacity coefficients matrix. Contour map of capacity coefficients are drawn as a function of the ratio between the radius and distance of two discs.