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.

$\blacksquare$

Sources

• 1990: I.S. Grant and W.R. Phillips: Electromagnetism (2nd ed.) ... (previous) ... (next): Chapter $1$: Force and energy in electrostatics: $1.2$ The Electric Field