Ratio of Electric to Gravitational Forces

Question:

A proton and an electron are separated by a distance d. There are two forces (electric force, Fe & gravitational force, Fg) acting on them. Why is the Fe/Fg ratio so large? What does it show? And why doesn't the value 'd' appear in this ratio, thus not affecting the results?

Answer:

The law of universal gravitation says that the force due to gravitational interaction between tow particles is proportional to the product of their masses divided by the square of the distance between them. From electrostatics we know that the force due to the electric interaction between two charged particles is proportional to the product of their charges divided by the square of the distance between them. Since both laws involve the square of the distance between the particles in the same way, the ratio of the forces will be independent of distance.

Since the distance drops out, the ratio of forces involves two quantities. One is the ratio of charge^2/mass^2. The other is the ratio of the electrostatic constant/gravitational constant. In devising a system of units we are free to select convenient quantities of charge and mass. Once that choice is made, the numerical values of the universal constants are measured in terms of the selected units by experiment. The significance of the huge ratio between electric and gravitational forces is that in our chosen system of units, the unit electric charge is much more effective at distorting the space around them than is the unit mass.

This information is brought to you by M. Casco Associates, a company dedicated to helping humankind reach the stars through understanding how the universe works. My name is James D. Jones. If I can be of more help, please let me know.

JDJ