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

(a) (i) The electric force between an electron and a proton at a distance r apart is
where the negative sign indicates that the force is attarctive the corresponding gravitation force
`F_(G)=-G(m_(p)m_(e))/(r_(3))`
however it may be mentioned here that the sign of the two forces are different of these forces between two protons inside a nucleus are `f_(e )-230 N` the ratio of the two forces shows that electrical forces are enormously stonger than the the gravitational forces
using newton second law of motion f=ma the acceleration that an electron will undergo is
comparing this with the value of acceleration due to gravity we can conclude that the effect of gravitationall field is negligible on the motion of electron under the action of coulomb force due ot a proton the value fro acceleartion of the proton is
`2.3xx10^(8)N//1.67 xx10^(27) kg =1.4 xx10^(19) m//s^(2)`