Magnitude of Electric Field caused by Point Charge

Theorem
Let $q$ be a point charge.

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

The magnitude of the electric field strength due to $q$ at $P$ is given by:

Then:
 * $\size {\map {\mathbf E} {\mathbf r} } = \dfrac {\size q} {4 \pi \epsilon_0 r^2}$

where:
 * $r$ is the distance $P$ is from $q$
 * $\varepsilon_0$ denotes the vacuum permittivity.

Proof
The following diagram shows the points of equal magnitude of $\map {\mathbf E} {\mathbf r}$ as dotted circles:


 * Field-lines-positive-charge.png