Coulomb’s Law Example Problem 1

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:

Coulomb Force equation

q1 and q2 is the amount of charge in Coulombs
r is the distance in meters between the charges
k is the Coulomb’s Law constant = 8.99×109 N•m2/C2

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?

First, draw a force diagram of the problem.

Setup diagram of Coulomb's Law Example Problem.
Two charges separated by one centimeter experiencing a force of repulsion of 90 N.

Define the variables:
F = 90 N
q1 = charge of first body
q2 = charge of second body
r = 1 cm

Use the Coulomb’s Law equation

Coulomb Force equation

The problem says the two charges are identical, so

q1 = q2 = q

Substitute this into the equation

Coulomb Example Problem Step

Since we want the charges, solve the equation for q

Coulomb Example Problem math step 3

Coulomb Example Problem Math Step 4

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.

Coulomb Example math step 5

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.

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

For another Coulomb’s law example problem, check out Coulomb Force Example Problem.