1. Problem: Find the distance between two point charges $q_1 = 26.0 \times 10^{-6}$ C and $q_2 = -47 \times 10^{-6}$ C such that the electrostatic force between them is 5.7 N. 2. Formula: Coulomb's law states that the magnitude of the electrostatic force $F$ between two point charges is given by $$F = k \frac{|q_1 q_2|}{r^2}$$ where $k = 8.99 \times 10^9$ N m$^2$/C$^2$ is Coulomb's constant, and $r$ is the distance between the charges. 3. Rearranging to solve for $r$: $$r^2 = k \frac{|q_1 q_2|}{F}$$ 4. Substitute the values: $$r^2 = 8.99 \times 10^9 \times \frac{|26.0 \times 10^{-6} \times (-47 \times 10^{-6})|}{5.7}$$ 5. Calculate the numerator inside the fraction: $$|26.0 \times 10^{-6} \times (-47 \times 10^{-6})| = 26.0 \times 47 \times 10^{-12} = 1222 \times 10^{-12} = 1.222 \times 10^{-9}$$ 6. Substitute back: $$r^2 = 8.99 \times 10^9 \times \frac{1.222 \times 10^{-9}}{5.7}$$ 7. Simplify the fraction: $$\frac{1.222 \times 10^{-9}}{5.7} = 2.144 \times 10^{-10}$$ 8. Multiply: $$r^2 = 8.99 \times 10^9 \times 2.144 \times 10^{-10} = 1.927$$ 9. Take the square root: $$r = \sqrt{1.927} = 1.388 \text{ meters}$$ **Final answer:** The distance between the charges must be approximately $1.39$ meters.