Coulomb’s Law is a force law between charged bodies. It relates the force to the magnitude and charges on the two bodies and the distance between them by the relationship:

where

q_{1} and q_{2} is the amount of charge in Coulombs r is the distance in meters between the charges k is the Coulomb’s Law constant = 8.99×10^{9} N•m^{2}/C^{2}

The direction of the force depends on the positive or negative charges on the bodies. If the two charges are identical, the force is a repulsive force. If one is positive and the other negative, the force is an attractive force.

This Coulomb’s Law example problem shows how to use this equation to find the charges necessary to produce a known repulsive force over a set distance.

Example Problem: The force between two identical charges separated by 1 cm is equal to 90 N. What is the magnitude of the two charges?

Solution: First, draw a force diagram of the problem.

Define the variables: F = 90 N q_{1} = charge of first body q_{2} = charge of second body r = 1 cm

Use the Coulomb’s Law equation

The problem says the two charges are identical, so

q_{1} = q_{2} = q

Substitute this into the equation

Since we want the charges, solve the equation for q

Enter the values of the problem for each variable into this equation. Remember to convert 1 cm to 0.01 meters to keep the units consistent.

q = ±1.00×10^{-6} Coulombs

This equation has two possible answers. The charges can both be positive or both negative and the answer will be the same for the repulsive Columb force over a distance of 1 cm.

Answer: Two identical charges of ±1.00×10^{-6} Coulombs separated by 1 cm produce a repulsive force of 90 N.