1. **State the problem:** Two spheres exert a force of 20 N on each other when separated by 6 m. One sphere has twice the charge of the other. We need to find the charge on each sphere. 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 $F$ is the force, $k = 9 \times 10^9$ Nm$^2$/C$^2$ is Coulomb's constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them. 3. **Set variables:** Let the smaller charge be $q$, then the larger charge is $2q$. 4. **Substitute values:** $$20 = 9 \times 10^9 \times \frac{|q \times 2q|}{6^2}$$ 5. **Simplify:** $$20 = 9 \times 10^9 \times \frac{2q^2}{36}$$ 6. **Simplify fraction:** $$20 = 9 \times 10^9 \times \frac{\cancel{2}q^2}{\cancel{36}18}$$ 7. **Isolate $q^2$:** $$20 = \frac{9 \times 10^9 \times 2 q^2}{36} \Rightarrow 20 = 5 \times 10^8 q^2$$ 8. **Solve for $q^2$:** $$q^2 = \frac{20}{5 \times 10^8} = 4 \times 10^{-8}$$ 9. **Find $q$:** $$q = \sqrt{4 \times 10^{-8}} = 2 \times 10^{-4}$$ 10. **Final charges:** Smaller charge $q = 2 \times 10^{-4}$ C Larger charge $2q = 4 \times 10^{-4}$ C Thus, the charges are $2 \times 10^{-4}$ C and $4 \times 10^{-4}$ C respectively.