对孤立椭球导体面电荷密度与表层曲率之间关系的研究

The Relationship Research between the Surface Charge Density and Curvature for an Ellipsoidal Conductor

对于孤立椭球导体,即处于静电平衡作用下,而椭球导体面上电荷密度的分布规律在理论分析上一直都是一个比较复杂的静电学问题,人们普遍认为,孤立的椭球导体面上的电荷密度上的电荷密度随着表面曲率半径的增大而增大,而确定的比例关系一直没有定量得出.本文将通过理论计算得出导体表面曲率与电荷密度之间的定量关系.首先,用平面曲率来表示曲面的曲率,其次,计算正圆柱面、旋转双曲面和旋转抛物面的曲率.最后确定带电孤立椭球面电荷密度与表层曲率关系,认为对于一般的孤立椭球导体,面电荷密度与表层曲率的1/4次方成正比,这表明了电荷大的地方电荷密度也大,同时电荷密度不仅与H存在一定的比例关系,而且还和导体的空间角度存在一定的关系,即不同的空间角度对应着不同的面电荷密度值.

For isolated ellipsoid conductor ,when it is in a charge density on the ellipsoid conductor in theory have problems. It is commonly believed that the surface charge an ellipsoidal conductor but haven＇t obtain a certain result. theoretical calculation. static balance always been a function, the distribution of more complex electrostatic density is direct proportion to curvature of This paper will draw a conclusion through