Electrical Force Calculation Using Coulomb's Law
In the realm of physics, understanding the fundamental forces that govern the interactions between charged particles is paramount. One such force is the electrical force, a cornerstone of electromagnetism. This article delves into the calculation of the electrical force acting between two charges, leveraging Coulomb's Law, a foundational principle in electrostatics. We will dissect the problem, elucidating each step involved in determining the magnitude of this force. By applying Coulomb's Law and meticulously substituting the given values, we aim to provide a comprehensive understanding of the underlying physics and arrive at the correct solution. This exploration is crucial for anyone seeking to grasp the intricacies of electromagnetism and its applications in various fields of science and engineering.
At the heart of our discussion lies the electrical force, a manifestation of the electromagnetic interaction between charged particles. This force, often referred to as the electrostatic force, can be either attractive or repulsive, depending on the signs of the charges involved. Unlike charges attract, while like charges repel, a principle that underpins a vast array of phenomena, from the structure of atoms to the behavior of electrical circuits. To quantify this force, we turn to Coulomb's Law, a cornerstone of electrostatics. Coulomb's Law provides a mathematical framework for calculating the magnitude of the electrical force between two point charges. It states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Mathematically, this law is expressed as:
F = k * |q1 * q2| / r^2
Where:
- F represents the magnitude of the electrical force.
- k is Coulomb's constant, approximately 8.9875 × 10^9 N⋅m2/C2.
- q1 and q2 denote the magnitudes of the two charges.
- r signifies the distance separating the charges.
This equation encapsulates the essence of electrostatic interactions, highlighting the critical role of charge magnitudes and separation distance in determining the strength of the force. Understanding and applying Coulomb's Law is essential for tackling a wide range of problems in electromagnetism.
Let's consider a specific scenario to illustrate the application of Coulomb's Law. We have two charges: one with a magnitude of -3 × 10^-6 C and another with a magnitude of 4 × 10^-6 C. These charges are separated by a distance of 0.025 meters. The objective is to determine the electrical force, denoted as F, acting on these charges. This problem serves as a practical exercise in applying Coulomb's Law and reinforces the concepts discussed earlier. By systematically substituting the given values into the equation, we can calculate the magnitude of the electrical force and gain a deeper understanding of the interaction between these charged particles.
To calculate the electrical force, we will utilize Coulomb's Law, which, as discussed earlier, is given by the formula:
F = k * |q1 * q2| / r^2
Where:
- F is the electrical force we aim to find.
- k is Coulomb's constant, approximately 8.9875 × 10^9 N⋅m2/C2. For simplicity, we'll often use the approximation 9 × 10^9 N⋅m2/C2.
- q1 and q2 are the magnitudes of the charges, which are 3 × 10^-6 C and 4 × 10^-6 C, respectively. Note that we use the absolute values of the charges since we're calculating the magnitude of the force.
- r is the separation distance between the charges, which is 0.025 meters.
Now, we substitute these values into Coulomb's Law:
F = (9 × 10^9 N⋅m2/C2) * |(3 × 10^-6 C) * (4 × 10^-6 C)| / (0.025 m)^2
First, let's calculate the product of the charge magnitudes:
|(3 × 10^-6 C) * (4 × 10^-6 C)| = 12 × 10^-12 C^2
Next, we square the distance:
(0. 025 m)^2 = 0.000625 m^2
Now, we substitute these results back into the equation:
F = (9 × 10^9 N⋅m2/C2) * (12 × 10^-12 C^2) / (0.000625 m^2)
F = (9 × 12 × 10^-3 N⋅m^2) / (0.000625 m^2)
F = (108 × 10^-3 N⋅m^2) / (0.000625 m^2)
F = 0.108 Nâ‹…m^2 / 0.000625 m^2
Finally, we perform the division to find the magnitude of the force:
F = 172.8 N
Therefore, the electrical force acting on these charges is 172.8 Newtons. This result aligns with option A in the given choices.
In this article, we have successfully calculated the electrical force between two charges using Coulomb's Law. By meticulously applying the formula and substituting the given values, we determined that the force acting on the charges is 172.8 Newtons. This exercise underscores the importance of Coulomb's Law in understanding and quantifying electrostatic interactions. The step-by-step approach outlined in this article provides a clear framework for solving similar problems in electromagnetism. Furthermore, it highlights the significance of paying attention to units and ensuring consistency throughout the calculation process. The electrical force is a fundamental concept in physics, and mastering its calculation is crucial for comprehending a wide range of phenomena, from the behavior of charged particles to the operation of electrical devices. This exploration serves as a valuable stepping stone for those seeking to delve deeper into the fascinating world of electromagnetism and its applications.
