Problem 1: Find the force between charges q_{1} = +4 μC and q_{2} = −6 μC separated by r = 30 cm.

Step 1 — Identify given quantities with units: q_{1} = +4 μC = $4 \times 10^{-6}$ C q_{2} = −6 μC = $6 \times 10^{-6}$ C (magnitude) r = 30 cm = 0.30 m k = $9 \times 10^{9}$ N $m^{2}$ $C^{-2}$

Step 2 — Apply Coulomb's law (magnitude): $F = \frac{k|q_1||q_2|}{r^2} = \frac{9\times10^9\ \text{N m}^2\text{C}^{-2} \times 4\times10^{-6}\ \text{C} \times 6\times10^{-6}\ \text{C}}{(0.30\ \text{m})^2}$

Step 3 — Calculate numerator: Numerator = $9 \times 10^{9}$ × $4 \times 10^{-6}$ × $6 \times 10^{-6}$ = 9 × $24 \times 10^{-3}$ = $216 \times 10^{-3}$ = 0.216 N $m^{2}$

Step 4 — Calculate denominator: $r^{2}$ = (0.30)^{2} = 0.09 $m^{2}$

Step 5 — Final result: $F = \frac{0.216\ \text{N m}^2}{0.09\ \text{m}^2} = 2.4\ \text{N (attractive, since charges are opposite)}$