Electric Field caused by Point Charge

Theorem
Let $q$ be a point charge.

Let $\mathbf r_q$ be the position vector of $q$.

Let $\map {\mathbf E} {\mathbf r}$ be the electric field strength due to $q$ at a point $P$ whose position vector is $\mathbf r$.

Then:
 * $\ds \map {\mathbf E} {\mathbf r} = \dfrac 1 {4 \pi \epsilon_0} \dfrac {q \paren {\mathbf r - \mathbf r_q} } {\size {\mathbf r - \mathbf r_q}^3}$

where $\varepsilon_0$ denotes the vacuum permittivity.

Proof
A specific application of Electric Field Strength from Assemblage of Point Charges for $1$ point charge.