Electric Field caused by Point Charge

Theorem
Let $p$ be a charged particle whose electric charge is $q$.

Let $\mathbf r_p$ be the position vector of $p$.

Let $\map {\mathbf E} {\mathbf r}$ be the electric field strength due to $p$ 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_p} } {\size {\mathbf r - \mathbf r_p}^3} $

Proof
A specific application of Electric Field Strength from Assemblage of Charges for $1$ charged particle.