Lei de Coulomb - Aula 01 (Teoria e Exemplos)

Introduction

This tutorial provides a comprehensive overview of Coulomb's Law, including its theoretical foundations and practical examples. Understanding Coulomb's Law is essential for studying electrostatics and electrical interactions between charged particles.

Step 1: Understanding Coulomb's Law

Coulomb's Law describes the force between two charged particles. It states that:

• The force (F) between two point charges (q1 and q2) is directly proportional to the product of their charges.
• The force is inversely proportional to the square of the distance (r) between them.

Formula

The mathematical expression of Coulomb's Law is given by:

F = k * |q1 * q2| / r^2

Where:

• F is the force between the charges.
• k is Coulomb's constant (approximately 8.99 x 10^9 N m²/C²).
• q1 and q2 are the amounts of the charges.
• r is the distance between the centers of the two charges.

Practical Advice

• Ensure you use consistent units (Coulombs for charge, meters for distance).
• Remember that the force can be attractive or repulsive depending on the signs of the charges.

Step 2: Example 1 - Calculating the Force Between Two Charges

Let's work through an example to apply Coulomb's Law.

Given:

• Charge q1 = +2 µC (microcoulombs)
• Charge q2 = -3 µC
• Distance (r) = 0.05 m

Steps to Calculate:

1. Convert microcoulombs to coulombs:
   • q1 = 2 x 10^(-6) C
   • q2 = -3 x 10^(-6) C
2. Plug the values into the formula:

   F = (8.99 x 10^9 N m²/C²) * |(2 x 10^(-6) C) * (-3 x 10^(-6) C)| / (0.05 m)^2
   

3. Calculate the force:
   • Evaluate the numerator:

   |(2 x 10^(-6)) * (-3 x 10^(-6))| = 6 x 10^(-12)
   

   • Evaluate the denominator:

   (0.05)^2 = 0.0025
   

   • Calculate the force:

   F = (8.99 x 10^9) * (6 x 10^(-12)) / 0.0025
   

   • Resulting in:

   F = 2.1576 N (approximately)
   

Step 3: Example 2 - Force Between Two Point Charges

In this example, we'll consider two point charges separated by a distance of 1 mm.

Given:

• Charge q1 = +5 µC
• Charge q2 = +10 µC
• Distance (r) = 1 mm = 0.001 m

Steps to Calculate:

1. Convert values:
   • q1 = 5 x 10^(-6) C
   • q2 = 10 x 10^(-6) C
2. Use the formula:

   F = (8.99 x 10^9 N m²/C²) * |(5 x 10^(-6) C) * (10 x 10^(-6) C)| / (0.001 m)^2
   

3. Calculate:
   • Numerator:

   |(5 x 10^(-6)) * (10 x 10^(-6))| = 50 x 10^(-12)
   

   • Denominator:

   (0.001)^2 = 0.000001
   

   • Calculate the force:

   F = (8.99 x 10^9) * (50 x 10^(-12)) / 0.000001
   

   • Resulting in:

   F = 449.5 N (approximately)
   

Conclusion

Coulomb's Law is a fundamental principle in electrostatics that quantifies the interaction between charged particles. By applying the formula correctly and ensuring unit consistency, you can easily calculate the force between any two charges. For additional study, consider exploring more complex scenarios or applications of Coulomb's Law in real-world contexts, such as electric fields and forces in circuits.