Exploring the Inverse Square Law and Electric Force Calculation

This article delves into the inverse square law, particularly as it applies to Coulomb's law and the electric force between charged particles. We will discuss the mathematical formulation, a practical example, and the reasoning behind the observed force changes when the distance between charges is altered.

The Inverse Square Law and Coulomb's Law

The inverse square law is a fundamental principle in physics, which describes how the intensity of various forces (such as gravitational or electric) decreases with distance. Coulomb's law is a specific application of the inverse square law to the electric force between two point charges. The law is mathematically expressed as:

Coulomb's Law: FC k frac{q_1 q_2}{r^2}

Where:

FC is the electric force between the two charges, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, r is the distance separating the charges.

Understanding the Inverse Square Law

The inverse square law states that the intensity of the force is inversely proportional to the square of the distance between the two interacting entities. This means that as the distance between two charges increases, the force between them decreases in an inverse square manner. For example, if the distance between two charges is doubled, the force between them is reduced to a quarter of its original value.

Practical Example and Calculation

Let's consider a specific scenario. Suppose two charged bodies exert a force of 3.2 × 10^-2 N on each other at a certain distance. The question asks: what will be the force between them if their separation is doubled?

First, we need to understand the formula.

Coulomb's Law: F k frac{q_1 q_2}{r^2}

Given:

Original force, F 3.2 times 10^{-2} text{ N} Distance, r New distance, 2r

According to the inverse square law, when the distance is doubled, the new force is given by:

F_{text{new}} k frac{q_1 q_2}{(2r)^2} k frac{q_1 q_2}{4r^2} frac{1}{4} left(k frac{q_1 q_2}{r^2}right) frac{1}{4} F

Therefore, if the distance is doubled, the electric force between the charges becomes a quarter of the original force.

Mathematically, this can be expressed as:

F_{text{new}} frac{1}{4} times 3.2 times 10^{-2} text{ N} 8 times 10^{-3} text{ N}

Sample Exercises and Further Reading

To better understand the inverse square law in action, let's solve a few sample exercises:

Exercise 1

Find the electric force between two charges of 2 C and 3 C if they are 5 meters apart.

Solution:

F k frac{q_1 q_2}{r^2} 8.99 times 10^9 frac{(2 text{ C})(3 text{ C})}{(5 text{ m})^2} 8.99 times 10^9 frac{6 text{ C}^2}{25 text{ m}^2} 2.16 times 10^9 text{ N}sqrt{m^2 text{C}^2 / N} approx 2.16 times 10^9 text{ N}

Exercise 2

An electron and a positron, each with a charge of 1.6 × 10^-19 C, are separated by 2 meters. Calculate the force between them.

Solution:

F k frac{q_1 q_2}{r^2} 8.99 times 10^9 frac{(1.6 times 10^{-19} text{ C})^2}{(2 text{ m})^2} 8.99 times 10^9 frac{2.56 times 10^{-38} text{ C}^2}{4 text{ m}^2} 5.73 times 10^{-29} text{ N}

Conclusion

The inverse square law is a critical concept in physics, and understanding Coulomb's law is essential for grasping the behavior of electric forces between charged particles. By practicing sample exercises and applying the inverse square law, one can effectively calculate and predict the electric force between two charges based on their separation distance.

For further reading and detailed explanations, consider exploring textbooks on electromagnetism or enrolling in a physics course. Additionally, consulting a tutor or teacher can also provide valuable insights and guidance.