静电场唯一性定理是电动力学的重要内容.它是指给定研究区域内的电荷分布及电介质性质，给定边界上的电势或者电势的法向导数，那么空间的电场分布唯一确定(静磁场类似).它的证明方法很巧妙，但证明技巧有什么物理内涵？怎样推广到一般的方程和边界条件？大部分教材并未涉及.本文发现作用量与唯一性定理的证明密切相关，只要构造出满足相应运动方程和边界条件的作用量，就可以证明唯一性定理.本文进一步讨论了运动方程不是泊松方程的情况以及破坏唯一性定理的边界条件.

 The uniqueness theorem of the electrostatic field plays an essential role in electrodynamics. It states that the electric field can be determined uniquely, given the charge distribution and dielectric distribution of the area of our concern and given the potential or its normal derivative on the boundary. The proof of uniqueness theorem is tricky. However, most textbooks do not discuss the proof method's physical significance and the generalization to other fields. This paper finds that the action closely relates to the proof of uniqueness theorem. Once one constructs the action obeying the corresponding equations of motion and boundary conditions, one can prove the uniqueness theorem for any field. Furthermore, we discuss more general equations of motion and boundary conditions and study the case violating the uniqueness theorem.