Coulomb's Law - Net Electric Force & Point Charges

Introduction

This tutorial provides a comprehensive overview of Coulomb's Law, focusing on how to calculate the net electric force between two or three point charges. Understanding this fundamental physics concept is essential for high school and college students. We'll break down the steps for applying Coulomb's Law to various situations, along with practical examples to enhance your learning.

Step 1: Understanding Coulomb's Law

Coulomb's Law describes the electric force between two charged objects. The law states that:

• The electric force (F) is directly proportional to the product of the magnitudes of the charges (q1 and q2).
• The force is inversely proportional to the square of the distance (r) between the charges.

The formula is given by:

[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} ]

Where:

• F = electric force between the charges
• k = Coulomb's constant ((8.99 \times 10^9 , N \cdot m^2/C^2))
• ( q_1 ) and ( q_2 ) = magnitudes of the charges
• r = distance between the centers of the two charges

Practical Tips

• Ensure the charges are in Coulombs (C) and the distance is in meters (m) for accurate calculations.
• Remember that the direction of the force depends on the signs of the charges: like charges repel, while opposite charges attract.

Step 2: Calculating the Electric Force Between Two Charges

To calculate the electric force between two point charges:

1. Identify the values of the charges:

   • For example: ( q_1 = 3 , \mu C ) and ( q_2 = -2 , \mu C )

2. Convert microcoulombs to coulombs:

   • ( 3 , \mu C = 3 \times 10^{-6} C )
   • ( -2 , \mu C = -2 \times 10^{-6} C )

3. Determine the distance between the charges:

   • For example: ( r = 0.5 , m )

4. Substitute the values into the formula: [ F = 8.99 \times 10^9 \cdot \frac{|3 \times 10^{-6} \cdot -2 \times 10^{-6}|}{(0.5)^2} ]

5. Calculate the force:

   • Compute the numerator and denominator, then solve for F.

Common Pitfalls

• Double-check unit conversions to avoid calculation errors.
• Be mindful of the signs of the charges when determining the direction of the force.

Step 3: Calculating the Net Electric Force with Three Charges

When dealing with three charges, the net force is the vector sum of the forces acting on a particular charge.

1. Calculate the force between each pair of charges using Coulomb's Law:

   • For charges ( q_1, q_2, ) and ( q_3 ), calculate ( F_{12}, F_{13}, ) and ( F_{23} ).

2. Determine the direction of each force:

   • Use vector notation to account for direction, especially if charges are placed at different angles.

3. Sum the forces vectorially:

   • Combine the forces based on their directions to find the net force on the charge of interest.

Example Calculation

If ( q_1 = 3 , \mu C ), ( q_2 = -2 , \mu C ), and ( q_3 = 1 , \mu C ) are placed at specific coordinates, you would calculate each pair's force and then combine them appropriately.

Conclusion

Coulomb's Law is a crucial concept in understanding electric forces between charged objects. By following the steps outlined, you can calculate the electric force between two or three point charges effectively. Practice with various charge configurations and distances to strengthen your understanding. For further exploration, consider working through the provided worksheet and additional practice problems available through the resources linked in the video description.