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:
The equation of Coulomb’s law is:
Fe= k |q1|·|q2|/r2.
We substitute the values of the data we have gathered in the equation:
Fe=(8.99·109 Nm2/C2)·(1.60·10-19C)· (1.60·10-19C)/(5.29·10-11m)2=8.22·10-8N
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.