Electrostatic And Gravitational Forces Exploring Physics Exercise 1

Introduction

This article delves into two fundamental forces of nature: the electrostatic force and the gravitational force. We will explore these forces through a couple of intriguing problems. The first problem challenges us to determine the distance at which the repulsive electrostatic force between two electrons reaches a magnitude of one Newton. This exploration will require us to apply Coulomb's Law, a cornerstone of electrostatics. The second problem shifts our focus to a comparison between the electric and gravitational forces acting between an electron and a proton. This comparison will highlight the immense difference in strength between these two fundamental forces, showcasing the dominance of the electrostatic force at the atomic level. Understanding these forces is crucial for comprehending the behavior of matter and energy in the universe.

Problem 1: Distance for a One Newton Repulsive Force

In this first problem, our primary focus lies in calculating the distance at which the repulsive force between two electrons reaches a magnitude of one Newton. To solve this, we will employ Coulomb's Law, a fundamental principle governing the electrostatic interaction between charged particles. Coulomb's Law states that the electrostatic force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (q1 and q2) and inversely proportional to the square of the distance (r) separating them. Mathematically, this is expressed as:

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

where k is Coulomb's constant, approximately 8.9875 × 10^9 N⋅m^2/C2. In our specific scenario, both charges are electrons, each carrying a charge of approximately -1.602 × 10^-19 Coulombs. The force (F) is given as 1 Newton. Our objective is to determine the distance (r). To achieve this, we will rearrange Coulomb's Law to solve for r:

r = √ (k * |q1 * q2| / F)

Substituting the known values:

r = √ (8.9875 × 10^9 N⋅m^2/C2 * |-1.602 × 10^-19 C * -1.602 × 10^-19 C| / 1 N)

Calculating this expression, we arrive at a distance of approximately 1.52 × 10^-14 meters. This incredibly small distance underscores the immense strength of the electrostatic force at close range. The repulsive force between two electrons becomes substantial even at such minuscule separations, highlighting the importance of electrostatic interactions in atomic and molecular phenomena. This result demonstrates how Coulomb's Law allows us to quantify the electrostatic force and predict its behavior based on charge and distance. It serves as a crucial tool in understanding the interactions of charged particles in various physical systems. Furthermore, this calculation provides a concrete example of the magnitude of electrostatic forces at the subatomic level, reinforcing the concepts of charge, force, and distance in the realm of particle physics.

Problem 2: Comparing Electric and Gravitational Forces

The second part of our exploration involves a comparative analysis of the electric and gravitational forces between an electron and a proton. This comparison will vividly illustrate the vast disparity in strength between these two fundamental forces. The electric force, as we discussed earlier, is governed by Coulomb's Law. The gravitational force, on the other hand, is described by Newton's Law of Universal Gravitation, which states that the gravitational force (Fg) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) separating them. Mathematically, this is expressed as:

Fg = G * (m1 * m2) / r^2

where G is the gravitational constant, approximately 6.674 × 10^-11 N⋅m^2/kg2.

To compare these forces, we will calculate both the electric force (Fe) and the gravitational force (Fg) between an electron and a proton at a given distance. Let's consider a typical atomic distance, say 1 × 10^-10 meters. The electron has a charge of approximately -1.602 × 10^-19 Coulombs and a mass of approximately 9.109 × 10^-31 kg. The proton has a charge of approximately +1.602 × 10^-19 Coulombs and a mass of approximately 1.673 × 10^-27 kg. Applying Coulomb's Law, we can calculate the electric force:

Fe = k * |q_e * q_p| / r^2

Fe = (8.9875 × 10^9 N⋅m^2/C2 * |-1.602 × 10^-19 C * 1.602 × 10^-19 C|) / (1 × 10^-10 m)^2

Fe ≈ 2.307 × 10^-8 N

Now, let's calculate the gravitational force using Newton's Law of Universal Gravitation:

Fg = G * (m_e * m_p) / r^2

Fg = (6.674 × 10^-11 N⋅m^2/kg2 * 9.109 × 10^-31 kg * 1.673 × 10^-27 kg) / (1 × 10^-10 m)^2

Fg ≈ 1.014 × 10^-47 N

Comparing the magnitudes of these forces, we observe a staggering difference. The electric force (Fe ≈ 2.307 × 10^-8 N) is approximately 10^39 times stronger than the gravitational force (Fg ≈ 1.014 × 10^-47 N). This immense disparity underscores why electrostatic forces dominate interactions at the atomic and molecular levels. The gravitational force, while crucial for large-scale phenomena like planetary motion, is practically negligible compared to the electric force when dealing with individual atoms and molecules. This explains why atoms are held together by electromagnetic forces, forming molecules and ultimately the matter we observe around us. The overwhelming strength of the electric force is a fundamental aspect of the universe, shaping the structure and behavior of matter at its most basic level. This comparison highlights the distinct roles of these two fundamental forces in the cosmos.

Conclusion

Through these exercises, we have gained a deeper understanding of the electrostatic and gravitational forces. We calculated the distance at which the repulsive force between two electrons reaches one Newton, highlighting the strength of electrostatic interactions at close range. We also compared the electric and gravitational forces between an electron and a proton, revealing the overwhelming dominance of the electric force at the atomic level. These explorations reinforce the fundamental principles of physics and provide valuable insights into the nature of forces that govern our universe. Understanding these concepts is crucial for anyone seeking to delve deeper into the world of physics and the behavior of matter and energy.