Dielectrics
#Physics
Topics
$\displaystyle V(\vec{r})=k\left(\oint_{\mathcal{S}}\frac{\sigma_{b}}{\mathscr{r}}\mathrm{d}a'+\iiint_{\mathcal{V}} \frac{\rho_{b}}{\mathscr{r}}\mathrm{d}\tau'\right)$
$\displaystyle V(\vec{r})=k\int \frac{\vec{P}(r')\hat{\mathscr{r}}}{\mathscr{r}^{2}} , \mathrm{d}\tau'$
- 4.19 Griffiths
- Macroscopic potential for a dielectric
$$\displaystyle V_{\text{uniform sphere}}(r,\theta)=
\begin{cases}
\frac{P}{3{\varepsilon}{0}}r\cos \theta, & r\leq R \\\frac{P}{3{\varepsilon}{0}} \frac{R^{3}}{r^{2}}\cos \theta, & r\geq R
\end{cases}
$$
- $\displaystyle \theta$ is the angle between the polarization $\displaystyle \vec{P}$ and the point of interest