Coulomb's Law

Coulomb’s Law gives the electrostatic force between two particles:

Where is the unit vector pointing from to . Since it is a unit vector, , and .

We often use to denote . So,

called the electric constant or the electric permittivity of free space.

You can check the direction of force using the Fundamental Law of Charges.

In terms of The Electric Field,

Coulomb’s Law is an application of Gauss’s Law for force between two particles.

In electromagnetism, if you have more than one charge acting on a particle, you can just add the charges. This is not true for all forces (for example, the strong nuclear force). It is from this principle that we can perform calculus for Distributed Charges on Objects.

Example. Find the coulomb force on .

Description: we have three point charges. is at , is as in quadrant 1, and is at .

The total force on is , the force of on plus , the force of on .

We can find and .

Let’s rewrite our vectors to make the problem easier:

So

We can split this into and components.