diff options
Diffstat (limited to 'source/know/concept/clausius-mossotti-relation')
| -rw-r--r-- | source/know/concept/clausius-mossotti-relation/index.md | 6 |
1 files changed, 4 insertions, 2 deletions
diff --git a/source/know/concept/clausius-mossotti-relation/index.md b/source/know/concept/clausius-mossotti-relation/index.md index a0f4916..03bdcac 100644 --- a/source/know/concept/clausius-mossotti-relation/index.md +++ b/source/know/concept/clausius-mossotti-relation/index.md @@ -55,7 +55,8 @@ the dipole term will be dominant in that case, given by: $$\begin{aligned} V_i(\vb{r}) - \approx \frac{1}{4 \pi \varepsilon_0} \frac{1}{|\vb{r}|^2} \int \rho_i(\vb{r}') \: |\vb{r}'| \cos{\theta} \dd{\vb{r}'} + \approx \frac{1}{4 \pi \varepsilon_0} \frac{1}{|\vb{r}|^2} + \int_{-\infty}^\infty \rho_i(\vb{r}') \: |\vb{r}'| \cos{\theta} \dd{\vb{r}'} \end{aligned}$$ Where $$\theta$$ is the angle between $$\vb{r}$$ and $$\vb{r}'$$, @@ -64,7 +65,8 @@ with the unit vector $$\vu{r}$$, normalized from $$\vb{r}$$: $$\begin{aligned} V_i(\vb{r}) - = \frac{1}{4 \pi \varepsilon_0} \frac{1}{|\vb{r}|^2} \: \vu{r} \cdot \!\!\int \vb{r}' \rho_i(\vb{r}') \dd{\vb{r}'} + = \frac{1}{4 \pi \varepsilon_0} \frac{1}{|\vb{r}|^2} + \: \vu{r} \cdot \!\!\int_{-\infty}^\infty \vb{r}' \rho_i(\vb{r}') \dd{\vb{r}'} \end{aligned}$$ The integral is a more general definition of the dipole moment $$\vb{p}_i$$. |