Continuous Charge Distribution

• Generalizing Electric Field to a continuous distribution over a region

$$\mathbf{E}(\mathbf{r})=\frac{1}{4\pi {ϵ}_0}\int \frac{1}{r^2}dq$$

• Common forms include line charges, surfaces charges, and volume charges
• Volume charge distribution is also sometimes referred to using Coulomb’s Law

$$\mathbf{E}(\mathbf{r})=\frac{1}{4\pi {ϵ}_0}\int \frac{\rho ({\mathbf{r}}^{\prime })}{r^2}\hat{r}d{\tau }^{\prime }$$