Coupling Coulomb's Law in Action: Calculating Point Charges with Real-World Examples

The Laws of physics, such as Coulomb's Law, form the foundation of electrostatics. This principle describes how two charges exert a force on each other. Understanding and applying this concept can solve various problems in physics and engineering. In this article, we will delve into a practical problem involving point charges and illustrate how to calculate unknown charges using Coulomb's Law.

Introducing Coulomb's Law

Coulomb's Law is a fundamental law in physics that describes the force between two point charges. It is expressed mathematically as:

F k * q1 * q2 / r^2

Where:

F is the electrostatic force between the charges (in Newtons, N) q1 and q2 are the magnitudes of the point charges (in Coulombs, C) r is the distance between the charges (in meters, m) k is Coulomb's constant, approximately 9.0 × 10^9 N·m^2/C^2

A Practical Example: Calculating the Unknown Charge

Let's use a specific problem to demonstrate how Coulomb's Law can be applied in practice. The problem is as follows:

The distance between two point charges is 60 mm, and the repulsive force between them is 2 x 109 N. If one charge is 20 μC, what is the charge of the other point charge?

Given this information, let's solve the problem step-by-step:

Known Values: F 2 × 10^9 N q1 20 × 10^(-6) C 20 μC r 60 × 10^(-3) m 60 mm k 9.0 × 10^9 N·m^2/C^2 Applying Coulomb's Law: F k * q1 * q2 / r^2 2 × 10^9 (9 × 10^9) * (20 × 10^(-6)) * (q2) / (60 × 10^(-3))^2 Substitute the known values and simplify: 2 × 10^9 (9 × 10^9) * (20 × 10^(-6)) * (q2) / 0.036 2 × 10^9 (18 × 10^3) * (q2) / 0.036 2 × 10^9 5 × 10^4 * (q2) q2 2 × 10^9 / 5 × 10^4 Solve for q2: q2 4 × 10^5 / 10^4 40 C

Therefore, the charge of the other point charge is 40 C.

Understanding the Significance

This example showcases the practical application of Coulomb's Law in solving real-world problems. Understanding this concept is crucial in various fields such as electrical engineering, materials science, and physics. By mastering how to calculate unknown charges using Coulomb's Law, you can better comprehend the behavior of electrically charged particles in different scenarios.

Conclusion

In conclusion, Coulomb's Law is a fundamental principle in physics, and its application in calculating the force between charged particles is invaluable. Whether you're a student of physics or an engineer working on electrical systems, grasping this concept will enhance your understanding of electrostatics.