22.7 : Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To compare the numerical strengths of the first two, take two particles of the same kind. Since electrons are fundamental particles, they are a good example.

Since both are inverse square law forces, the distance gets canceled when the ratio of the two forces is considered. Instead, the ratio of the electrical and gravitational forces depends on the value of the natural constants, particularly the gravitational constant, the permittivity of vacuum, the electron's charge, and the electron's mass. It is enormous, about 4 followed by 42 zeroes. This numerical comparison reveals how weak the gravitational force is compared to its electromagnetic counterpart.

Although both the forces are inverse-square laws, there is a difference. The gravitational force is only attractive, whereas the electrical force can be attractive or repulsive. Since the latter is strong, it also implies that charged particles are accelerated by it, finally settling into a configuration with hardly any remnant electrical force. Hence, most objects around us are electrically neutral. Even astronomical objects, like the Earth and the Moon, are electrically neutral and do not exert electrical forces on each other.

An important corollary is that most everyday interactions are electromagnetic forces. For example, when one pushes the floor with their feet, they exert electromagnetic forces on the floor. The floor, in turn, exerts electromagnetic forces on the feet. Friction, which helps us walk and cars move, is an electromagnetic force. Moreover, since electrical forces are inverse square law, friction is important only at small interacting distances, explaining why we do not experience them all the time.

All chemical forces are electromagnetic. That is, all of chemistry, and by extension, biology, are governed by electromagnetic forces. Small remaining charges and charge distributions govern life and almost all interactions on Earth.

Although weak, the gravitational force cannot be neutralized because it is only attractive. Hence, gravitational forces persist at large distances, governing the motion of the Moon around the Earth, the planets' motion around the Sun, etc. It persists at interstellar, intergalactic, and cosmological distances, governing large-scale events in the universe.