Electric Field

An electric field $E$ is a vector field in space that represents the effect of electric forces towards a charged particle within it.

• The force on a body of charge $q$ placed in the field is given by $F=qE$
• The curl of any electric field results in $\nabla \times E=0$ because any electric field is a superposition of charges (or charge-distributions) that individually emit radial field lines that do not have curl

Relating Equations

$$E(r)=\frac{1}{4\pi ϵ\_0}\int \frac{q}{\vec{r}}\hat{\vec{r}},ds\text{ (with any differential)}$$

To ease this tedious integral, Gauss’ Law exists or one can calculate E over the Potential