Dielectrics

Topics

• Polarizability
• Electric Displacement
• Bound Charge Density

$V(\vec{r})=k\left({\oint }_{\mathcal{S}}\frac{{\sigma }_b}{r}\mathrm{d}{a}^{\prime }+{\iiint }_{\mathcal{V}}\frac{{\rho }_b}{r}\mathrm{d}{\tau }^{\prime }\right)$

$V(\vec{r})=k\int \frac{\vec{P}(r^{\prime })\hat{r}}{r^2}\mathrm{d}{\tau }^{\prime }$

• 4.19 Griffiths
• Macroscopic potential for a dielectric

$$\{\begin{array}{ll}\frac{P}{3{\epsilon }_0}r\cos \theta ,& r\le R\\ \frac{P}{3{\epsilon }_0}\frac{R^3}{r^2}\cos \theta ,& r\ge R\end{array}$$

• $\theta$ is the angle between the polarization $\vec{P}$ and the point of interest

${\vec{E}}_{\text{in uniform sphere}}=-\frac{\vec{P}}{3{\epsilon }_0}$