# Newton and Coulomb: Fatal Attractions and Fundamental Forces

Something that always fascinates me about physics teaching and learning is that the basic concepts are closely interrelated. If you can grasp the concepts of Newton’s laws of motion as applied to the acceleration of objects in one dimension, then this knowledge can be used to evaluate the motion of objects in a variety of situations, including the motion of charged particles in electric and magnetic fields.

Another case where the basic laws of physics are interrelated is in the realm of the very big and the very small. We see this in the example of Newton’s law of universal gravitation and Coulomb’s law.

Newton first published his law of universal gravitation in Philosophiæ Naturalis Principia Mathematica in 1687. The law states that the gravitational force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

As an inverse-square law, this law is analogous to Coulomb’s law, first published in 1785 by French physicist Charles-Augustin de Coulomb. It states that the electrical force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Although the laws have important differences, the equations look similar when seen side by side:

Each law is used to describe the forces between two objects, two masses in Newton’s case and two charges in Coulomb’s. Each law also contains a constant. For Newton’s law the constant G is quite small (6.67 ･ 10-11 Nm2/kg2) because the force of gravity is very weak. For Coulomb, the constant k is quite large (8.99 ･ 109 Nm2/C2) because the electric force is relatively large. In fact, the force of attraction between two 1 coulomb charges that are separated by a distance of 1 meter is one thousand trillion times greater than the force of attraction between two 1 kilogram masses separated by 1 meter. That is a very big difference!

One important difference between the two laws is that the force between two masses is always attractive, while the electric force between two charges can be either attractive or repulsive. Watch my latest video for a brief explanation of the difference between the two laws. And post a comment if you have any questions!

A great way to increase student knowledge of Newton’s law of gravitation and Coulomb’s law is through PhET online lab simulations. Students have fun with these simulations and Step by Step Science offers the companion activities shown below for students to practice what they learn.

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