1. **State the problem:** We have two spheres with charges $q_1$ and $q_2$, where one charge is twice the other, so $q_2 = 2q_1$. They are separated by a distance $r = 6$ m and exert a force $F = 20$ N on each other. We need to find $q_1$ and $q_2$. 2. **Formula used:** The force between two point charges is given by Coulomb's law: $$F = k \frac{|q_1 q_2|}{r^2}$$ where $k = 8.99 \times 10^9$ N m$^2$/C$^2$ is Coulomb's constant. 3. **Substitute $q_2 = 2q_1$ into the formula:** $$F = k \frac{|q_1 \cdot 2q_1|}{r^2} = k \frac{2q_1^2}{r^2}$$ 4. **Solve for $q_1^2$:** $$q_1^2 = \frac{F r^2}{2k}$$ 5. **Plug in the known values:** $$q_1^2 = \frac{20 \times 6^2}{2 \times 8.99 \times 10^9} = \frac{20 \times 36}{1.798 \times 10^{10}} = \frac{720}{1.798 \times 10^{10}}$$ 6. **Calculate $q_1^2$:** $$q_1^2 = 4.004 \times 10^{-8}$$ 7. **Take the square root to find $q_1$:** $$q_1 = \sqrt{4.004 \times 10^{-8}} = 2.0 \times 10^{-4}$$ 8. **Find $q_2$:** $$q_2 = 2q_1 = 2 \times 2.0 \times 10^{-4} = 4.0 \times 10^{-4}$$ **Final answer:** $$q_1 = 2.0 \times 10^{-4} \text{ C}, \quad q_2 = 4.0 \times 10^{-4} \text{ C}$$