# Example of Coulomb's law application

In this example, we will use Coulomb’s law to determine the electrostatic force between a proton and an electron in a very simplified classical model of the hydrogen atom.

**First, we will determine the magnitude** of the force using the equation of Coulomb’s law. **Then, we will determine the direction** of the force, using the part of Coulomb’s law that states that particles with opposite charges attract and particles with like charges repel.

The electrostatic force between two particles depends on:

- Constant of Coulomb’s law (
): This is simply a constant of proportionality, it is always the same every time we use Coulomb’s law. Its value in the SI is*k***8.99·10**.^{9}Nm^{2}/C^{2} - Charge of the first particle (
): We can take this as the*q*_{1}**electron**. The charge of the electron in the SI is**1.60·10**and it is^{-19}C**negative in sign**. - Change of the second particle (
): We can take this as the*q*_{2}**proton**. The charge of the proton in the SI is**1.60·10**and it is^{-19}C**positive in sign**. Notice that it is the same quantity of charge as the electron, but it has a different sign. - Distance between the particles (
): We will take this to be the radius of the hydrogen atom, which is*r***5.29·10**.^{-11}m

The equation of Coulomb’s law is:

F_{e}= k |q_{1}|·|q_{2}|/r^{2}.

We substitute the values of the data we have gathered in the equation:

F_{e}=(8.99·10^{9} Nm^{2}/C^{2})·(1.60·10^{-19}C)· (1.60·10^{-19}C)/(5.29·10^{-11}m)^{2}=**8.22·10 ^{-8}N**

This is the **magnitude** of the electrostatic force.

Now, we must determine its **direction**. The force acts **along the line that joins the two particles**, but it could be an attractive force (which pulls them together) or a repulsive force (that drives them apart). The electron and the proton have charges of **opposite signs**. Because opposite charges **attract**, the force pulls the electron and the proton together, acting in the line that joins them. That is the direction of the electrostatic force.

**Figure:** Simplified version of the hydrogen atom. The arrows point in the direction of the electrostatic forces in this situation.