Question 21.75: The charges of an electron and a positron are -e and +e. The......

The electrical force between an electron and a positron separated by a distance r is $F_e=k e^2 / r^2$. On the other hand, the gravitational force between the two charges is $F_g=G m_e^2 / r^2$. Thus, the ratio of the two forces is

$\frac{F_e}{F_g}=\frac{k e^2 / r^2}{G m_e^2 / r^2}=\frac{k e^2}{G m_e^2}=\frac{\left(8.99 \times 10^9 \,N \cdot m ^2 / C ^2\right)\left(1.6 \times 10^{-19} C \right)^2}{\left(6.67 \times 10^{-11} \,N \cdot m ^2 / kg ^2\right)\left(9.11 \times 10^{-31} \,kg \right)^2}=4.16 \times 10^{42}$.