Content deleted Content added
→Proof: Equation numbering and linking |
|||
Line 18:
It follows that <math>\varphi=\varphi_2-\varphi_1</math> is a solution of [[Laplace's equation]], which is a special case of [[Poisson's equation]] that equals to <math>0</math>. By subtracting the two solutions above gives
{{NumBlk||<math display="block">\mathbf{\nabla}^2 \varphi = \mathbf{\nabla}^2 \varphi_1 - \mathbf{\nabla}^2 \varphi_2 = 0. </math>|{{EquationRef|1}}}}
Line 34 ⟶ 33:
By applying the [[divergence theorem]], we rewrite the expression above as
{{NumBlk||<math display="block">\int_{S} (\varphi \, \mathbf{\nabla}\varphi) \cdot \mathrm{d}\mathbf{S}= \int_V (\mathbf{\nabla}\varphi)^2 \, \mathrm{d}V. </math>|{{EquationRef|2}}}}
| |||