# Coulomb's Law

Confusing concepts?

Concepts and terms on this page are explored more intuitively in the Altitude Analogy page. If you're confused like I was, give it a read if you haven't already!

## Electrostatic Force

Coulomb's law is an inverse-square law which defines the electrostatic force between two charged particles. It suggests that as the distance between two charged particles doubles, the force between them is four times weaker.

The equivalent for gravitational fields is gravitational force, calculated using Newton's law of universal gravitation.

Formula

Variable Key

• $F$ is electrostatic force, in newtons.
• ${Q}_{1}$ and ${Q}_{2}$ are the charges of the respective particles, in coulombs.
• ${\epsilon }_{0}$ is the vacuum permittivity constant.
• $r$ is the distance between the particles, in metres.

Attract or repel?

If the calculated electrostatic force is positive, then the charged particles are repelling each other (since both ${Q}_{1}$ and ${Q}_{2}$ will have the same sign), and vice versa - if the electrostatic force is negative, then the charged particles are attracting each other.

### Finding the Distance Between Particles

The above formula can be rearranged to make $r$ the subject, as shown below:

The Naïve Approach

However, this won't work if the charges are attracting each other, as the fraction under the square root would be negative and $r$ would be undefined (or technically a complex number). To get around this, we have to take the absolute value of the numerator:

## Vacuum Permittivity

Vacuum permittivity, also known as permittivity of free space or the electric constant, is a constant which determines how easy it is for an electric field to "penetrate" a vacuum, and consequently how strongly charges influence each other. The greater the permittivity, the easier it is for charges to interact, and the less electrostatic force is therefore required.

Permittivity is represented by the Greek letter epsilon, $\epsilon$.