Superposition of Electrostatic Forces Quiz with Answer Key

📚 Quick Study Guide

• ⚡ The principle of superposition states that the net electrostatic force on a charge due to multiple other charges is the vector sum of the individual forces.
• 📏 Mathematically, if you have $n$ charges exerting forces on a charge $q$, the net force $\vec{F}_{net}$ is given by: $\vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + ... + \vec{F}_n$.
• ➕ Each individual force $\vec{F}_i$ can be calculated using Coulomb's Law: $\vec{F}_i = k \frac{|q_i q|}{r_i^2} \hat{r}_i$, where $k$ is Coulomb's constant ($8.99 \times 10^9 N m^2/C^2$), $q_i$ is the charge exerting the force, $q$ is the charge experiencing the force, $r_i$ is the distance between the charges, and $\hat{r}_i$ is the unit vector pointing from $q_i$ to $q$.
• 📐 Remember to resolve forces into components (x and y) when adding them vectorially. Use trigonometry ($\sin(\theta)$, $\cos(\theta)$) to find these components.
• 💡 Ensure all units are consistent (Coulombs for charge, meters for distance, and Newtons for force).

🧪 Practice Quiz

1. A charge of +2μC is placed 3m to the left of a -5μC charge. What is the direction of the electrostatic force on the +2μC charge?
   1. To the left
   2. To the right
   3. Upward
   4. Downward
2. Two identical positive charges, each with a magnitude of 3μC, are placed 4m apart. What is the magnitude of the electrostatic force between them?
   1. 4.05 x 10⁻³ N
   2. 5.06 x 10⁻³ N
   3. 6.07 x 10⁻³ N
   4. 7.08 x 10⁻³ N
3. A +4μC charge is placed at the origin. A -6μC charge is placed at x = 2m. What is the net electrostatic force on a +1μC charge placed at x = 1m?
   1. -0.216 N
   2. 0.216 N
   3. -0.108 N
   4. 0.108 N
4. Three charges are arranged in an equilateral triangle. Charge A (+2μC) is at the top vertex, charge B (-3μC) is at the lower left, and charge C (+5μC) is at the lower right. If the sides of the triangle are 0.5m, what is the direction of the net force on charge A?
   1. Left
   2. Right
   3. Downward
   4. Upward
5. A charge of +5 nC is located at (0,0), and a charge of -2 nC is located at (3,0). What is the x-component of the net force on a +1 nC charge located at (6,0)?
   1. -0.125 nN
   2. 0.125 nN
   3. -0.250 nN
   4. 0.250 nN
6. Two charges, +q and -q, are separated by a distance d. What is the magnitude of the electrostatic force between them if the distance is doubled?
   1. F/4
   2. F/2
   3. 2F
   4. 4F
7. A charge of +3μC is located at (1,1), and a charge of -4μC is located at (4,5). What is the approximate direction of the force on the +3μC charge?
   1. Up and to the right
   2. Down and to the left
   3. Up and to the left
   4. Down and to the right