why we take r squared (r²) in coulomb and gravitation law??? why we take r² rather than r etc...
Answers
A lot of things decrease in intensity as 1/r2, such as light intensity, gravity, charge forces, etc. This is because the same force needs to act over a larger spherical area. The further away, the larger the sphere. And you should know that the surface area of a sphere is SA=4πr2. Since the area varies as r2, dividing the magnitude of the intensity by the area means it drops as 1/r2.
This is an experimentally observed fact and later this equation is developed. Many of the equations we use in physics has either experimental Base or some are just theoretical where it is not possible to perform experiment. It is common practice to simplify the look of several other equations by changing the form a selected equation. The full version of the denominator is 4 pi r^2. Physicists remove 4 pi leaving only the r^2 term. The 4 pi becomes part of the proportionality constant k. Later, other equations that make use of Coulomb’s equation have the leaner look of r^2. The 4 pi travels as part of k.