Electric Force Calculation Between Two Charges Using Coulomb's Law

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In the realm of physics, understanding the fundamental forces that govern the interactions between charged particles is crucial. One such force is the electric force, a cornerstone of electromagnetism. This article delves into the calculation of the electric force between two charges, providing a step-by-step guide and exploring the underlying principles. We will use a specific example to illustrate the process, offering a clear and comprehensive explanation for students and enthusiasts alike. Understanding Coulomb's Law is essential for grasping the concepts presented here, as it forms the basis for calculating the electric force. This article aims to break down the complexities of electrostatics and make it accessible to a broader audience.

Understanding Electric Force and Coulomb's Law

The electric force is a fundamental force of nature that governs the interaction between electrically charged objects. It is one of the four known fundamental forces, alongside the strong nuclear force, the weak nuclear force, and the gravitational force. Unlike gravity, which is always attractive, the electric force can be either attractive or repulsive, depending on the charges involved. Objects with like charges (both positive or both negative) repel each other, while objects with opposite charges (one positive and one negative) attract each other. The strength of the electric force is described by Coulomb's Law, a cornerstone of electrostatics.

Coulomb's Law, named after French physicist Charles-Augustin de Coulomb, mathematically quantifies the electric force between two point charges. It states that the electric force (F) between two 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) between them. This relationship can be expressed by the following equation:

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

where:

• F is the magnitude of the electric force
• k is Coulomb's constant, approximately equal to 9.00 × 10^9 N⋅m^2/C2
• q1 and q2 are the magnitudes of the charges
• r is the distance between the charges

The absolute value signs around the product of the charges ensure that we are dealing with the magnitude of the force. The direction of the force (attractive or repulsive) is determined by the signs of the charges themselves. This inverse square relationship is a crucial aspect of Coulomb's Law, highlighting how rapidly the electric force diminishes with increasing distance. Grasping this relationship is paramount for anyone studying electrostatics. It's not just about plugging numbers into a formula; it's about understanding the underlying physics.

Problem Statement: Calculating the Electric Force

Let's consider a specific problem to illustrate the application of Coulomb's Law. We have two charges: one with a charge of 0.0072 C (q1) and another with a charge of -0.0060 C (q2). These charges are separated by a distance of 0.0040 m (r). Our goal is to calculate the electric force (F) acting between these two charges. To solve this, we'll use the formula from Coulomb's Law:

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

where k = 9.00 × 10^9 N⋅m^2/C2. This problem provides a practical scenario for applying our understanding of Coulomb's Law. It's important to note the units involved – Coulombs (C) for charge, meters (m) for distance, and Newtons (N) for force. Keeping track of units is essential for accurate calculations in physics. This example allows us to move beyond the theoretical and delve into the practical application of electrostatics principles. We will meticulously walk through each step of the calculation to ensure clarity and understanding. This approach will help solidify your grasp of how Coulomb's Law works in a real-world context. It also emphasizes the importance of careful problem-solving techniques in physics. By breaking down the problem into manageable steps, we can avoid errors and arrive at the correct answer.

Step-by-Step Solution

Now, let's break down the calculation step-by-step.

1. Identify the given values:

   • q1 = 0.0072 C
   • q2 = -0.0060 C
   • r = 0.0040 m
   • k = 9.00 × 10^9 N⋅m^2/C2

2. Plug the values into Coulomb's Law:

   $F = (9.00 × 10^9 N⋅m^2/C^2) * |(0.0072 C) * (-0.0060 C)| / (0.0040 m)^2$

3. Calculate the product of the charges:

   |(0. 0072 C) * (-0.0060 C)| = 4.32 × 10^-5 C^2

   Note the absolute value, which makes the product positive.

4. Square the distance:

   (0.0040 m)^2 = 1.6 × 10^-5 m^2

5. Substitute the calculated values back into the equation:

   $F = (9.00 × 10^9 N⋅m^2/C^2) * (4.32 × 10^-5 C^2) / (1.6 × 10^-5 m^2)$

6. Perform the multiplication and division:

   $F = (9.00 × 10^9 * 4.32 × 10^-5) / (1.6 × 10^-5) N$ $F = 388800 / 1.6 × 10^-5 N$ $F = 2.43 × 10^10 × 10^5 N$ $F = 2.43 × 10^5 N$

7. Determine the direction of the force:

   Since the charges have opposite signs (one positive and one negative), the electric force is attractive. However, because we only calculated the magnitude using the absolute values, we need to consider the signs of the charges to determine the direction. In this case, since the charges are opposite, the force is attractive.

This meticulous breakdown ensures that each step is clear and easily followed. By working through the problem in this way, you can gain a deeper understanding of how Coulomb's Law is applied in practice. The importance of using the correct units throughout the calculation cannot be overstated. A mistake in units can lead to a completely wrong answer. This step-by-step approach also helps to minimize errors and provides a clear pathway to the correct solution. Understanding the sign conventions and their implications on the direction of the force is just as important as calculating the magnitude.

Result and Discussion

Based on our calculations, the magnitude of the electric force acting between the two charges is approximately 2.43 × 10^10 N. Since the charges are of opposite signs, this force is attractive. This result highlights the immense strength of the electric force, even at relatively small distances. The force is positive, which indicates that the charges are attracting each other, aligning with the fundamental principles of electrostatics. It’s crucial to remember that the magnitude of the force alone doesn’t tell the whole story; the direction is equally important. The attractive nature of the force in this scenario is a direct consequence of the opposite charges involved.

This example serves as a practical demonstration of Coulomb's Law and its implications. The calculated force is substantial, underscoring the significance of electrostatic interactions in various physical phenomena. From the behavior of atoms and molecules to the operation of electronic devices, the electric force plays a pivotal role. This understanding is fundamental not only in physics but also in fields like chemistry, materials science, and engineering. The ability to accurately calculate and interpret electric forces is a valuable skill for anyone pursuing these disciplines. Further exploration of electrostatics might involve analyzing systems with multiple charges or investigating the electric field, a concept closely related to the electric force. This particular calculation lays the groundwork for more complex problems in electromagnetism and highlights the interconnectedness of various concepts in physics.

Conclusion

In conclusion, we have successfully calculated the electric force between two charges using Coulomb's Law. The result demonstrates the magnitude and direction of the force, highlighting the fundamental principles of electrostatics. This step-by-step guide provides a clear understanding of the calculation process and reinforces the importance of Coulomb's Law in physics. The problem-solving approach used here can be applied to a wide range of electrostatic problems, making it a valuable tool for students and professionals alike. A solid grasp of Coulomb's Law is essential for further studies in electromagnetism and related fields. This example illustrates the power of mathematical models in describing and predicting physical phenomena. It also underscores the importance of careful attention to detail when solving physics problems. By breaking down complex problems into smaller, manageable steps, we can gain a deeper understanding of the underlying principles. Furthermore, the application of these principles extends beyond the classroom and into various real-world applications, highlighting the practical significance of electrostatics. Continuing to explore and apply these concepts will undoubtedly lead to a more profound appreciation of the world around us.