Strength of the Electric Interaction

If two electrons or two protons are separated by a distance of one centimeter, then according to Equation 1 there is a repulsive force between them whose strength is 2.3 ×10^–19 dynes. Since a dyne is the weight of one milligram of mass, 2.3 ×10^–19 dynes is a very small force. But, of course, protons and electrons are very small particles.

..........(1)
To get a better idea of how strong the electric force is, let us compare it with the gravitational force. If we have 2 protons any distance r apart, then the ratio of the electric repulsion to the gravitational attraction is

..........(2)

Since both electricity and gravity are 1/r² forces, the r² cancel out in Equation 2 and we are left with

......(2)

The electrical force is some 10³⁶ times stronger than gravity. This is true no matter how far apart the protons are. The only reason that electric forces do not completely swamp gravitational forces is that there are both attractive and repulsive electric forces which tend to cancel on a large scale, when many electrons and protons are involved.