A Puzzling Observation in Physics
The gravitational attraction of protons is approximately a factor 1035 weaker than the electromagnetic repulsion.
This factor is independent of distance, because both forces are inversely proportional to the square of the distance.
Therefore on an atomic scale mutual gravity is negligible.
However, the main force beween common objects and the earth and between celestial bodies is gravity; this is due to the fact that they (at least one of the two) are electrically neutral to a high degree.
Newton's Law of Universal Graviation
F = Gm1m2/r2
F = force between the two bodies with mass 1 and mass 2
G = universal constant, same for all objects = 6.67x10-11 N·m2/kg2
r is the distance between the two bodies
Coulomb's Law
F = kQ1Q2/r2
F = magnitude of the electric force that each of two charged particles exert on each other
k is the proportionality constant= 8.988x109N·m2/C2 where C is coulombs
Q is the charge of each of the particles
r is the distance between the particles
The Numbers
Charge of proton (positive) = 1.6x10-19 C
Mass of Proton: 1.67x10-27 kg
Coulomb Force = FC Gravitational Force = FG Note: r is not included because it affects both the same way
FC = kQ1Q2/r2 ð 8.988x109N·m2/C2 (1.6x10-19 C)(1.6x10-19 C) = 1.67x10-29 N·m2
FG = Gm1m2/r2 ð 6.67x10-11 N·m2/kg2(1.67x10-27 kg)(1.67x10-27 kg) = 1.7x10-64N·m2
ð FC is about 1035 times stronger than FG
Demonstration: Small magnet picking up a potentiometer.
Question: How can a small magnet overcome the force of gravity exerted by the Earth on a potentiometer?