Question

Find the ratio of the electrical and gravitational forces between two protons.

Answer 1

We know that the mass of a proton, m = 1.67 × 10⁻²⁷ kg
Charge on a proton, q = 1.6 × 10⁻¹⁹ C
Gravitational constant, $\mathrm{G}=6.67\times {10}^{-11}\mathrm{N}-{\mathrm{m}}^2/{\mathrm{kg}}^2$
Electrostatic force,
$F_e=\frac{1}{4\mathrm{\pi }{\epsilon }_0}\frac{q^2}{r^2}$
Gravitational force,
$$\begin{gathered} F_g=G\frac{m^2}{r^2} \\ \Rightarrow \frac{F_e}{F_g}=\frac{q^2}{4\mathrm{\pi }{\epsilon }_{0}G{m}^2} \\ =\frac{9\times {10}^9\times {\left(1.6\times {10}^{-19}\right)}^2}{6.67\times {10}^{-11}\times {\left(1.67\times {10}^{-27}\right)}^2} \\ =1.23\times {10}^{36} \end{gathered}$$