Two identical charges repel with 0.2 N at 9 cm separation. Find their force at 3 cm.

Solution & explanation

1. Given: F₁ = 0.2 N; r₁ = 9 cm; r₂ = 3 cm; charges and medium unchanged.

2. For unchanged charges, force varies inversely as distance squared.

   $$\frac{F_2}{F_1}=\frac{{r_1}^2}{{r_2}^2}$$

3. Multiply both sides by F₁.

   $$F_2=F_1\times {\left(\frac{r_1}{r_2}\right)}^2$$

4. Use the ratio in matching units; centimetres cancel.

   $$F_2=0.2\times {\left(\frac{9}{3}\right)}^2$$

5. Divide the distances, then square.

   $$F_2=0.2\times 3^2=0.2\times 9$$

6. State the result with units: F₂ = 1.8 N, still repulsive.

F₂ = 1.8 N