Electric Field

Topics

• Electric Field of Ring
• Electric Field of Disk
• Electric Field of Plane

$\vec{E}(r\stackrel{⃗}{})=k\sum _i\frac{q_i}{|\overrightarrow{r_i}{|}^3}\overrightarrow{r_i}$

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

• $k$ is the Coloumb Constant
• Separation Vector

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

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

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

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

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

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

$\vec{E}=-\nabla V-{\partial }_t\vec{A}$

• Time-dependent version
• $\vec{A}$ is the vector potential