Electric field

The electric field describes the electrostatic potential produced by a charge.

Point charge

For point charge $A$, its field at point $B$ in space is:

$$\vec E_{A \to B} = \frac{1}{4\pi\epsilon_0}\frac{Q_A}{\left\| AB \right\|^2}\widehat{AB}$$

Continuous charge

A charged conductor can be approximated as an infinite number of point charges $dQ$, each creating an electric field at arbitrary point in space $A$:

$$ \vec E_{dQ \to A} = \frac{1}{4\pi\epsilon0}\frac{Q}{\left\| \overrightarrow{PA} \right\|}\widehat{PA} $$

Therefore, the overall electric field at point $A$ is:

$$ \int \vec E_{dQ} dQ $$

Application

The electrostatic force experienced by a point charge $B$ is:

$$\vec F_e=Q_B\vec E_B$$