1. **State the problem:** We have three charges: $Q_1 = +13$ nC, $Q = +7$ nC, and $Q_2 = +11$ nC. Charge $Q$ is placed midway between $Q_1$ and $Q_2$, which are 17 cm apart. We need to find the magnitude and direction of the net force on charge $Q$. 2. **Identify distances:** Since $Q$ is midway, the distance from $Q$ to each charge is half of 17 cm: $$r = \frac{17}{2} = 8.5 \text{ cm} = 0.085 \text{ m}$$ 3. **Calculate forces due to each charge on $Q$ using Coulomb's law:** Coulomb's law formula: $$F = k \frac{|Q_1 Q_2|}{r^2}$$ where $k = 8.99 \times 10^9 \text{ Nm}^2/\text{C}^2$. - Force by $Q_1$ on $Q$: $$F_1 = 8.99 \times 10^9 \times \frac{(13 \times 10^{-9})(7 \times 10^{-9})}{(0.085)^2}$$ Calculate numerator: $$13 \times 7 = 91$$ Calculate denominator: $$0.085^2 = 0.007225$$ So, $$F_1 = 8.99 \times 10^9 \times \frac{91 \times 10^{-18}}{0.007225} = 8.99 \times 10^9 \times 1.259 \times 10^{-14} = 1.132 \times 10^{-4} \text{ N}$$ - Force by $Q_2$ on $Q$: $$F_2 = 8.99 \times 10^9 \times \frac{(11 \times 10^{-9})(7 \times 10^{-9})}{(0.085)^2}$$ Calculate numerator: $$11 \times 7 = 77$$ So, $$F_2 = 8.99 \times 10^9 \times \frac{77 \times 10^{-18}}{0.007225} = 8.99 \times 10^9 \times 1.066 \times 10^{-14} = 9.58 \times 10^{-5} \text{ N}$$ 4. **Determine direction of forces:** All charges are positive, so forces are repulsive. - $F_1$ pushes $Q$ away from $Q_1$. - $F_2$ pushes $Q$ away from $Q_2$. Since $Q$ is between $Q_1$ and $Q_2$, $F_1$ pushes $Q$ toward $Q_2$ and $F_2$ pushes $Q$ toward $Q_1$. 5. **Calculate net force:** The forces are in opposite directions along the line connecting the charges. Assuming right direction is from $Q_1$ to $Q_2$: - $F_1$ points right. - $F_2$ points left. Net force magnitude: $$F_{net} = |F_1 - F_2| = |1.132 \times 10^{-4} - 9.58 \times 10^{-5}| = 1.74 \times 10^{-5} \text{ N}$$ Direction: Since $F_1 > F_2$, net force is toward $Q_2$ (to the right). **Final answer:** The magnitude of the force on charge $Q$ is approximately $$1.7 \times 10^{-5} \text{ N}$$ and it is directed away from $Q_1$ toward $Q_2$.