| 通过拉普拉斯方程求解有特殊电荷分布的空间电势 |
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| 引用本文： | 肖星星,陈跃刚,付康印.通过拉普拉斯方程求解有特殊电荷分布的空间电势[J].贵州大学学报(自然科学版),2009,26(2):5-9. |
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| 作者姓名： | 肖星星 陈跃刚 付康印 |
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| 作者单位： | 贵州大学,贵州省光电子技术与应用重点实验室,贵州,贵阳,550025 |
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| 基金项目： | 贵州省自然科学基金资助项目，贵州大学基金(贵大人基合字 |
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| 摘 要： | 探讨的是空间有自由电荷分布时通过拉普拉斯方程求解空间电势分布的问题。当空间有自由电荷分布且电荷分布有一定特殊性时（球对称），可以将空间各点的电势看作是自由电荷在空间产生的电势与介质上的极化电荷在空间产生的电势相叠加。自由电荷在空间产生的电势可以用高斯（M．E．Gauss）定理进行求解，介质上的极化电荷在空间产生的电势分布满足拉普拉斯方程，可以用分离变量法求解。这样就把空间中有自由电荷分布时需求解的泊松方程的问题转化为拉氏方程进行求解，使问题得到简化。
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| 关 键 词： | 电势 泊松方程 拉普拉斯方程 高斯定理 分离变量法 |
Solution of the Electric Potential in the Space with Free Electric Charge Special Distribution by Laplace's Equation |
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| XIAO Xing-xing,CHEN Yue-gang,FU Kang-ying.Solution of the Electric Potential in the Space with Free Electric Charge Special Distribution by Laplace's Equation[J].Journal of Guizhou University(Natural Science),2009,26(2):5-9. |
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| Authors: | XIAO Xing-xing CHEN Yue-gang FU Kang-ying |
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| Institution: | Key Laboratory of Photoelectron Technology and Application;Guizhou University;Guiyang 550025;China |
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| Abstract: | The electric potential in the space with free electric charge special distribution(symmetry of sphere) was solved by Laplace's equation.In this case,the spatial potential was considered of superposition by the potential produced by free electric charges and polarized charges.While the potential produced by free electric charges could be solved with Gauss's Law,and the potential produced by polarized charges was depicted by Laplac's equation which can solved by the separation-of-variable method.As a result,P... |
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| Keywords: | electric potential Poisson's equation laplace's equation gauss's law separation-of-variable method |
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