物理

邦邦角的一补充

$\Large{\color{cornflowerblue}

{The~Dipole-Dipole~Interaction}}$

$\mathbf{N}$个电偶极子的静电能:

                           $\mathit{W}=-\frac{1}{2}\sum_{i=1}^{\mathit{N}}\vec{\mathit{p}_{i}}~\cdot~\vec{\mathit{E}}(\vec{\mathit{r}_{i}})$

$\mathit{W}=-\frac{1}{8\pi\varepsilon_{0}}\sum_{i=1}^{\mathit{N}}\sum_{j~\neq~i}^{\mathit{N}}\left\{\frac{\vec{\mathit{p}_{i}}~\cdot~\vec{\mathit{p}_{j}}}{|\vec{\mathit{r}_{i}}-\vec{mathit{r}_{j}}}|^{3}}-\frac{3\vec{\mathit{p}_{i}}~\cdot~(\vec{\mathit{r}_{i}}-\vec{\mathit{r}_{j}})\vec{\mathit{p}_{j}}~\cdot(\vec{\mathit{r}_{i}}-\vec{\mathit{r}_{j}})}{|\vec{\mathit{r}_{i}}-\vec{\mathit{r}_{j}}|^{5}}\right\}$