Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges/masses. Compare the strength of these forces by determining the ratio of their magnitudes (i) for an electron and a proton and (ii) for two protons

Explanation

(i) The electric force between an electron and a proton at a distance r apart is :
`F_(e)=-1/(4pi epsi_(0)) e^(2)/r^(2)`
Where the negative sign indicates that the force is attractive. The corresponding gravitational force (always attractive) is :
`F_(G)=-G (m_(p) m_(e))/r^(2)`
where `m_(p)` and `m_(e)` are the masses of a proton and an electron respectively.
`|F_(e)/F_(G)|=e^(2)/(4pi epsi_(0) Gm_(p) m_(e))=2.4xx10^(39)`
(ii) On similar lines, the ratio of the magnituds of electric force to the gravitational force between two protons at a distance r apart is :
`|F_(e)/F_(G)|=e^(2)/(4pi epsi_(0) Gm_(p) m_(e))=1.3xx10^(36)`
However, it may be mentioned here that the signs of the two forces are different. For two protons, the gravitational force is attractive in nature and the Coulomb force is repulsive. The actual values of these forces between two protons inside a nucleus (distance between two protons is `~10^(-15) m` inside a nucleus) are `F_(e) ~ 230 N` whereas `F_(G)~1.9xx10^(-34) N`.
The (dimensionaless) ratio of the two shows that electrical forces are enormously stronger than the gravitational forces.