Coulomb's Law

The French Physicist Charles Coulomb investigated the properties of force and charges. He discovered that the electrical force between two charges varies directly as the size of the charge and inversely as the square of the distance between them. We write this equation today as Coulomb's Law:

where F is the force of attraction (or repulsion) in Newtons, q represents the magnitude of the charges, in Coulombs, r is the distance between the charges in meters, and k is a proportionality constant:

k = 8.99 x 109 N m2/C2

A charge of 1 Coulomb (C) is HUGE - the force produced by two 1 C charges 1 meter apart would be about 9 billion Newtons. The charge on an electron is 1.602 x 10 -19 C. This is called the elementary charge, e.

Anybody see a similarity here between Coulomb's Law and Newton's Law of Universal Gravitation? Both obey that ever important inverse square relationship for force vs. distance, but there are a couple of very important points:

  • Gravitational forces are always forces of attraction (masses are always positive!)  Electric force can be either an attraction or a repulsion depending on the sign of the charges. Again, like charges repel (so a positive value of force would imply repulsion) while unlike charges attract (or a negative value of force indicates the charges are attracting each other.) Personally, I like to just use positive numbers and figure out the repulsion/attraction component after I have the magnitude of the Force.
  • Electric force is considerably stronger than gravitational force. It takes a relatively small amount of charge to overcome the force of gravity. Look at the number of electrons in a coulomb, figure out their mass, and look at the gravitational force for the example above. It's a lot smaller than 9 billion Newtons.

So how does it work? Consider two charges (let's say two electrons) separated by a distance of 0.5 x 10-10 meters. What is the Electric force between them?

The force is given by Coulomb's Law, and since the charges are both the same (negative), they will repel each other. Plugging in some numbers:

F = (8.99 x 109 N m2/C2) (1.6 x 10 -19 C)(1.6 x 10 -19 C)/ 0.5 x 10-10 m2.  This equals 8.2 x 10-8 N.

k can also be expressed in terms of the permittivity of free space, eo. k = 1/4peo

Problem solving using Coulomb's law.

These are force problems and are solved by adding the forces and using vectors, if necessary, to show the relative magnitude and direction of each particle's force on another particle. The resultant force on a charge is the vector sum of all of the forces on that charge. This is called the Principle of Superposition.

By the way, if you want to read what some infinitely smarter people than I have had to say about Coulomb's Law, try following one of the below links:

For Practice Problems, Try:

Electric Charge Problem

Giancoli Multiple Choice Practice Questions (Go ahead - try a few.)