Uniqueness theorem for Poisson's equation: Difference between revisions

Revision as of 17:35, 6 January 2021

Revision as of 17:35, 6 January 2021

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:<math>\mathbf{\nabla}^2 \varphi = -\frac{\rho_f}{\epsilon_0},</math>

where <math>\varphi</math> is the [[electric potential]] and <math>\rho_f</math> is the [[charge density|charge distribution]] over some region $<math>V$</math> with boundary surface $<math>S$</math> .

The uniqueness of the solution can be proven for a large class of boundary conditions as follows.