Determine the ratio of the electric and gravitational forces between two protons.

Step-by-step solution

The electric force between two protons separated by a distance r is given by Coulomb's law: F_e = 1 4 ₀ e^2 r^2 The gravitational force between them is given by Newton's law of gravitation: F_g = G m_p^2 r^2 The ratio of the two forces is: F_e F_g = e^2 4 ₀ G m_p^2 Substituting the standard values: e = 1.6 10⁻¹⁹ C 1 4 ₀ = 9 10^9 N m ^2/ C ^2 G = 6.67 10⁻¹¹ N m ^2/ kg ^2 m_p = 1.67 10⁻²⁷ kg F_e F_g = 9 10^9 (1.6 10⁻¹⁹)^2 6.67 10⁻¹¹ (1.67 10⁻²⁷)^2 F_e F_g = 9 2.56 10⁻²⁹ 6.67 2.7889 10⁻⁶⁵ F_e F_g = 23.04 18.60 10³⁶ 1.