Coulomb’s Law states that like charges repel and opposite charges attract with a force proportional to the product of the charges and inversely proportional to the square of the distance between them.

Despite the simplicity of the statement of Coulomb’s Law, it is far reaching in its application, and it describes many aspects of electric fields: what they are; how they react and the like.

To understand Coulomb’s Law and the interaction of electric charges and the resulting electric field a little more, it is possible to look at the basic concepts first and then building up from this.

It is found that an electric charge has an associated electric field and this interacts with other changes with their electric fields.

In terms fo the forces it is found that the electric force is greater if the strength of the charges is greater, i.e. charges are greater. It is also greater if the charges are closer together, and decrease if they are further away from each other. Specifically, the electric force is inversely proportional to the square of the distance between the two charges, i.e. it is an “inverse square law.”

Often the electric field lines are shown in diagrams and these indicate the electric field present at any given location.

## Coulomb’s Law formula

It is often necessary to be able to express laws such as Coulomb’s Law in the form of a formula or equation.

This enables a greater understanding of the law and it also enables various calculations to be made.

F = k Q1 Q2 / d2

**Where:**

F = force between the two charged objects in Newtons

Q_{1} = charge on object 1 in coulombs

Q_{2} = charge on object 2 in coulombs

k = Coulomb’s law constant. The value of this constant is depends on the medium in which the charged objects are immersed. For air the value is approximately 9.0 x 10^{9} N • m^{2} / C^{2}.

d = distance between two objects in metres.

It is worth noting that Coulomb’s law provides an accurate description of the force between two objects that can be considered as point charges. Fortunately a charged conducting sphere acts with other charged objects as though all of its charge were located at its centre, and hence it can be considered as a point charge.

As Coulomb’s law applies to point charges, the distance d in the equation above should be measured between the centres of the spheres for both objects. It is not the distance between the surfaces of the spheres. In some cases there may not bae a large difference between the two distances, but in others there will be. It is also important because the distance value is squared in the equation, and hence any discrepancies will be magnified in terms of the effect on the overall value of force.