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.
(a) Compare the strength of these forces by determining the ratio of their magnitudes
(i) for an electron and proton and
(ii) for two protons.
(b) Estimate the accelerations of electrons and protons due to the electrical force of the mutual attraction when they are `1 A^(o) = (10^(-10)m)` apart? `(m_(p) = 1.67 xx 10^(-27)kg) m_(e) = 9.11 xx 10^(-31)kg.

Explanation

a) i) The electric force between an electron and a proton at a distance . r. apart is
.F_e = - (1)/(4 pi epsilon) * (e^2)/(r^2).
The negative sign indicates that the force is attractive . The correspondingly gravitational force (also attractive)
.F_G = - (G(m_p)(m_e))/(r^2).
.:. |(F_e/F_G )| = (1)/(4piepsilon) * (e^2 *r^2)/(r^2*G*(m_p)*(m_e)) =e^2/(4piepsilon*G*(m_p)*(m_e).
= . 2.4 * 10^19.