# Coulomb's Law

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.

is **electrostatic force**, in newtons.and are the **charges of the respective particles**, in coulombs.is the **vacuum permittivity**constant.is the **distance between the particles**, in metres.

If the calculated electrostatic force is **positive**, then the charged particles are **repelling** each other (since both **negative**, then the charged particles are **attracting** each other.

### Finding the Distance Between Particles

The above formula can be rearranged to make

However, this won't work if the charges are attracting each other, as the fraction under the square root would be negative and *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,