## Conceptual Physics (12th Edition)

$F = 2.25 \times 10^{9} N$
Coulomb's Law is an inverse-square law, meaning the force is inversely proportional to the square of the distance. If the distance between the charges is doubled, the force is divided by a factor of 4. We simply divide the previous answer by 4. We can also calculate it directly, and obtain the same answer. Use Coulomb's Law, $F = k \frac{q_{1} \; q_{2}}{d^{2}}$. $$F = 9.0 \times 10^{9} \frac{N m^{2}}{C^{2}} \frac{q_{1} \; q_{2}}{d^{2}}$$ $$F = 9.0 \times 10^{9} \frac{N m^{2}}{C^{2}} \frac{(0.1 C)(0.1 C)}{(0.2 m)^{2}}$$ $$F = 2.25 \times 10^{9} N$$