Solution:

For no net force, electrostatic force must equal gravitational force: \( \frac{q^2}{4 \pi \varepsilon_0 r^2} = \frac{G m^2}{r^2} \). Rearranging this formula yields \( \frac{q^2}{m^2} = 4 \pi \varepsilon_0 G \Rightarrow \frac{q}{m} = \sqrt{4 \pi \varepsilon_0 G} \).