Coulomb's Law of Electrostatics

Physical Law

 * Coulombs-Law.png

Let $a$ and $b$ be stationary particles, each carrying an electric charge of $q_a$ and $q_b$ respectively.

Then $a$ and $b$ exert a force upon each other whose magnitude and direction are given by Coulomb's law (of electrostatics):


 * $\mathbf F_{a b} \propto \dfrac {q_a q_b {\mathbf r_{a b} } } {r^3}$

where:
 * $\mathbf F_{a b}$ is the force exerted on $b$ by the electric charge on $a$
 * $\mathbf r_{a b}$ is the displacement vector from $a$ to $b$
 * $r$ is the distance between $a$ and $b$.
 * the constant of proportion is defined as being positive.

By exchanging $a$ and $b$ in the above, it is seen that $b$ exerts the same force on $a$ as $a$ does on $b$, but in the opposite direction.

Permittivity of Free Space
Thus the equation becomes:
 * $\mathbf F_{a b} = \dfrac 1 {4 \pi \varepsilon_0} \dfrac {q_a q_b {\mathbf r_{a b} } } {r^3}$

Also presented as

 * $\mathbf F_{a b} \propto \dfrac {q_a q_b \hat {\mathbf r}_{a b} } {r^2}$

where $\hat {\mathbf r}_{a b}$ is the unit vector in the direction from $a$ to $b$.

Also known as
Coulomb's Law of Electrostatics is also known as just Coulomb's Law.