Solved Examples: Calculating Electric Force Between Charges

📚 Quick Study Guide

• ⚛️ Coulomb's Law: The electric force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
• 📐 Formula: $F = k \frac{|q_1 q_2|}{r^2}$, where:
  • $F$ is the electric force (in Newtons)
  • $k$ is Coulomb's constant ($k ≈ 8.9875 × 10^9 N m^2/C^2$)
  • $q_1$ and $q_2$ are the magnitudes of the charges (in Coulombs)
  • $r$ is the distance between the charges (in meters)
• ➕ Sign Convention: Like charges repel, and opposite charges attract. Remember to consider the direction of the force based on the signs of the charges.
• 📏 Units: Ensure all quantities are in SI units (Coulombs for charge, meters for distance, and Newtons for force).
• 💡 Superposition: If there are multiple charges, the net force on a particular charge is the vector sum of the forces due to all other charges.

🧪 Practice Quiz

1. What happens to the electric force between two charges if the distance between them is doubled?
   1. A. It doubles.
   2. B. It quadruples.
   3. C. It is reduced to one-half.
   4. D. It is reduced to one-quarter.
2. Two charges, $q_1 = +2\,\mu C$ and $q_2 = -4\,\mu C$, are separated by a distance of 3 m. What is the magnitude of the electric force between them?
   1. A. 0.008 N
   2. B. 0.08 N
   3. C. 0.0008 N
   4. D. 0.8 N
3. If the magnitude of both charges is doubled, and the distance remains the same, what happens to the electric force?
   1. A. It doubles.
   2. B. It quadruples.
   3. C. It remains the same.
   4. D. It is halved.
4. Which of the following is the correct unit for electric charge?
   1. A. Ampere
   2. B. Volt
   3. C. Coulomb
   4. D. Ohm
5. What is the direction of the electric force between a positive and a negative charge?
   1. A. Attractive
   2. B. Repulsive
   3. C. No force
   4. D. Depends on the magnitude of the charges
6. Two equal positive charges are placed at a certain distance. A third positive charge is placed exactly in the middle. What is the net force on the third charge?
   1. A. Towards the left
   2. B. Towards the right
   3. C. Zero
   4. D. Depends on the magnitude of the charges
7. What is the value of Coulomb's constant (k) approximately?
   1. A. $9 \times 10^9 N m/C$
   2. B. $9 \times 10^9 N m^2/C^2$
   3. C. $9 \times 10^{-9} N m^2/C^2$
   4. D. $9 \times 10^{-9} N m/C$