Coulomb’s Law is a force law between charged bodies. It relates the force to the magnitude and charge 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.

Two charges separated by one centimeter experiencing a force of repulsion of 90 N.

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 for q

Enter the values for the variables. Remember to convert 1 cm to 0.01 meters to keep the units consistent.

q = ±1.00×10^{-6} Coulombs

Since the charges are identical, they are either both positive or both negative. This force will be repulsive.

**Answer:**

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.

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