\[ \vec{E} = ( \, - \frac {\partial \phi} {\partial x} , - \frac {\partial \phi}{\partial y} , - \frac {\partial \phi}{\partial z} ) \]
\[ ( \, \vec{E} = - grad \, \phi = - \nabla \phi \, ) \]
\( \Longrightarrow \) 場所 \( \vec{x} \) の電荷 \( q \) は，位置エネルギーが (\ ｑ\,φ( \vec{x} ) \)。
- ポアッソン方程式
\[ \frac {\partial^2 \phi} {\partial x^2} + \frac {\partial^2 \phi}{\partial y^2} + \frac {\partial^2 \phi}{\partial z^2} = - \frac{\rho }{\epsilon_0} \]
\[ \left( \, \Delta \phi = - \frac{\rho }{\epsilon_0} \, \right) \]
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