Ethan's Notes

    Electric Field

    #Physics

    Topics

    $\displaystyle \vec{E}(\mathscr{r}\vec{})=k\sum_{i} \frac{q_{i}}{\lvert \vec{\mathscr{r}{i}}\rvert^{3}}\vec{\mathscr{r}{i}}$

    $\displaystyle \vec{E}=k\int \frac{1}{\mathscr{r}^{2}}\hat{\mathscr{r}} , \mathrm{d}q$

    $\displaystyle \vec{E}=k\int \frac{\lambda}{\mathscr{r}^{2}}\hat{\mathscr{r}} , \mathrm{d}l$

    • Electric field of line charge
    • $\displaystyle \lambda$ is the linear charge density

    $\displaystyle \vec{E}=k\int \frac{\rho}{\mathscr{r}^{2}}\mathscr{\hat{r}} , \mathrm{d}\tau$

    • Electric field of volume charge
    • $\displaystyle \rho$ is the volume charge density
    • $\displaystyle \tau$ is an infinitesimal volume element

    $\displaystyle \nabla \times \vec{E}=0$

    • This states that the curl of an electric field is 0 when considering only charges and not magnetic fields

    $\displaystyle \vec{E}=-\nabla V-\partial_{t}\vec{A}$