Understanding the Impact of Charge and Distance on Coulomb’s Law

Coulomb's Law, a cornerstone principle in the field of electrostatics, establishes the relationship between the forces experienced by two charged objects. This article delves into the specific scenario where the charges between two objects are halved and the distance between them is tripled, examining the resultant force in detail. We will explore the mathematical principles behind this phenomenon and conduct a step-by-step analysis to clarify any confusion.

Introduction to Coulomb’s Law

Coulomb's Law describes the force between two charged particles. The law is expressed as:

F k q1 q2 / r^2

Where:

F is the force between the charges, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, r is the distance between the charged particles.

Scenario Analysis

Let's consider a scenario where two charged objects experience a force of 36 N. If the charges are both halved and the distance between them is tripled, we need to determine the new force between them.

Initial Conditions

F 36 N q1 q2 are the initial charges r is the initial distance between the charges

Application of Coulomb's Law with New Conditions

First, we express the initial force using Coulomb's Law:

F k q1 q2 / r^2

Now, let's adjust the charges and distance:

q1 becomes q1/2 q2 becomes q2/2 r becomes 3r

Using these new conditions, we can write the new force as:

F' k (q1/2) (q2/2) / (3r)^2

Let's simplify this expression:

F' k q1 q2 / (2 * 2 * 9 * r^2)

F' k q1 q2 / 36r^2

We know from the initial state that:

F k q1 q2 / r^2 36 N

Thus:

F' 36 N / 36 1 N

Conclusion

By following the process of substituting the new values into Coulomb's Law, we find that the new force between the two charged objects is 1 N. This example beautifully illustrates how changes in the charges and distance between two objects directly impact the force experienced between them.

Understanding Coulomb's Law is crucial for many areas of physics and engineering, from everyday electrical devices to complex systems in physics and materials science. If you have any further questions or need additional clarifications, feel free to ask in the comments below.