Answer to Question #115863 in Astronomy | Astrophysics for Julia french

Question

When the gravitational force of attraction between 2 protons is compared to the electrostatic force of repulsion between the 2 protons, the electrostatic force of repulsion will be what?

Answer 1

Compare the magnitudes of forces of interaction between two protons at the same distance. Gravitational force:

$$F_g=G\frac{m_p^2}{r^2}.$$

Electrical force:

$$F_e=k\frac{e^2}{r^2}.$$

Divide the electrical by the gravitational:

$$\frac{F_e}{F_g}=\frac{ke^2}{Gm_p^2}=\\ \space\\=\frac{(1/(4\pi\epsilon_0))(1.602\cdot10^{-19})^2}{(6.673\cdot10^{-11})(1.673\cdot10^{-27})^2}=1.236\cdot10^{36}.$$

The electrical force is 10³⁶ times stronger than the gravitational one.