What Is The Electrical Force Between $q_1$ And $q_2$?Recall That $k = 8.99 \times 10^9 \, \text{N} \cdot \frac{\text{m}^2}{\text{C}^2}$.Given:- $q_1 = +6 \, \text{C}$- $q_2 = -4 \, \text{C}$- $q_3 = +3

by ADMIN 202 views

Introduction

When dealing with charged particles, understanding the forces that act between them is crucial in various fields of physics, including electromagnetism and particle physics. The electrical force, also known as the Coulomb force, is a fundamental force of nature that arises between charged particles. In this article, we will explore the concept of the electrical force between two charged particles and provide a step-by-step guide on how to calculate it.

What is the Electrical Force?

The electrical force is a force that acts between two charged particles, such as electrons and protons, or between a charged particle and a neutral object. It is a result of the interaction between the electric fields generated by the charged particles. The electrical force is a conservative force, meaning that it can be calculated using the concept of potential energy.

Coulomb's Law

Coulomb's Law is a mathematical formula that describes the electrical force between two charged particles. It is named after Charles-Augustin de Coulomb, who first discovered it in the 18th century. The law states that the electrical force between two charged particles is proportional to the product of the charges and inversely proportional to the square of the distance between them.

The Formula for Coulomb's Law

The formula for Coulomb's Law is given by:

F=kq1q2r2F = k \frac{q_1 q_2}{r^2}

where:

  • FF is the electrical force between the two charged particles
  • kk is Coulomb's constant, which is equal to 8.99×109 Nâ‹…m2C28.99 \times 10^9 \, \text{N} \cdot \frac{\text{m}^2}{\text{C}^2}
  • q1q_1 and q2q_2 are the charges of the two particles
  • rr is the distance between the two particles

Calculating the Electrical Force

To calculate the electrical force between two charged particles, we need to know the charges and the distance between them. Let's consider an example where we have two charged particles with charges q1=+6 Cq_1 = +6 \, \text{C} and q2=−4 Cq_2 = -4 \, \text{C}, and the distance between them is r=2 mr = 2 \, \text{m}.

Step 1: Plug in the values into the formula

We can now plug in the values into the formula for Coulomb's Law:

F=kq1q2r2F = k \frac{q_1 q_2}{r^2}

F=(8.99×109 N⋅m2C2)(6 C)(−4 C)(2 m)2F = (8.99 \times 10^9 \, \text{N} \cdot \frac{\text{m}^2}{\text{C}^2}) \frac{(6 \, \text{C})(-4 \, \text{C})}{(2 \, \text{m})^2}

Step 2: Simplify the expression

We can now simplify the expression by multiplying the numbers:

F=(8.99×109 N⋅m2C2)−24 C24 m2F = (8.99 \times 10^9 \, \text{N} \cdot \frac{\text{m}^2}{\text{C}^2}) \frac{-24 \, \text{C}^2}{4 \, \text{m}^2}

F=(8.99×109 N⋅m2C2)(−6 C2⋅1m2)F = (8.99 \times 10^9 \, \text{N} \cdot \frac{\text{m}^2}{\text{C}^2}) (-6 \, \text{C}^2 \cdot \frac{1}{\text{m}^2})

Step 3: Calculate the final value

We can now calculate the final value by multiplying the numbers:

F=−53.94×109 NF = -53.94 \times 10^9 \, \text{N}

F=−5.394×1011 NF = -5.394 \times 10^{11} \, \text{N}

Conclusion

In this article, we have explored the concept of the electrical force between two charged particles and provided a step-by-step guide on how to calculate it using Coulomb's Law. We have also calculated the electrical force between two charged particles with charges q1=+6 Cq_1 = +6 \, \text{C} and q2=−4 Cq_2 = -4 \, \text{C}, and the distance between them is r=2 mr = 2 \, \text{m}. The final value of the electrical force is −5.394×1011 N-5.394 \times 10^{11} \, \text{N}.

Frequently Asked Questions

  • What is the electrical force? The electrical force is a force that acts between two charged particles, such as electrons and protons, or between a charged particle and a neutral object.
  • What is Coulomb's Law? Coulomb's Law is a mathematical formula that describes the electrical force between two charged particles.
  • How do I calculate the electrical force? To calculate the electrical force, you need to know the charges and the distance between the two particles. You can use the formula for Coulomb's Law to calculate the electrical force.

References

  • Coulomb, C.-A. de. (1785). "Sur la force de la répulsion ou d'attraction des corps électrisés." Histoire de l'Académie Royale des Sciences, 361-387.
  • Griffiths, D. J. (2013). Introduction to Electrodynamics. Pearson Education.
  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.

Introduction

In our previous article, we explored the concept of electrical force and provided a step-by-step guide on how to calculate it using Coulomb's Law. However, we understand that there may be many questions and doubts that readers may have. In this article, we will address some of the frequently asked questions about electrical force.

Q: What is the electrical force?

A: The electrical force is a force that acts between two charged particles, such as electrons and protons, or between a charged particle and a neutral object.

Q: What is Coulomb's Law?

A: Coulomb's Law is a mathematical formula that describes the electrical force between two charged particles. It states that the electrical force between two charged particles is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Q: How do I calculate the electrical force?

A: To calculate the electrical force, you need to know the charges and the distance between the two particles. You can use the formula for Coulomb's Law to calculate the electrical force.

Q: What are the units of the electrical force?

A: The units of the electrical force are Newtons (N).

Q: What is the direction of the electrical force?

A: The direction of the electrical force is from the positive charge to the negative charge.

Q: Can the electrical force be attractive or repulsive?

A: Yes, the electrical force can be either attractive or repulsive, depending on the signs of the charges. If the charges have the same sign, the force is repulsive. If the charges have opposite signs, the force is attractive.

Q: What is the relationship between the electrical force and the distance between the charges?

A: The electrical force is inversely proportional to the square of the distance between the charges.

Q: Can the electrical force be zero?

A: Yes, the electrical force can be zero if the charges are equal and opposite, or if the distance between the charges is infinite.

Q: What is the significance of Coulomb's Law?

A: Coulomb's Law is a fundamental principle in physics that describes the behavior of charged particles. It has many practical applications in fields such as engineering, chemistry, and materials science.

Q: Can Coulomb's Law be applied to all types of charges?

A: No, Coulomb's Law is only applicable to point charges, which are charges that are concentrated at a single point.

Q: What is the difference between the electrical force and the gravitational force?

A: The electrical force and the gravitational force are two different types of forces that act between objects. The electrical force acts between charged particles, while the gravitational force acts between masses.

Q: Can the electrical force be measured?

A: Yes, the electrical force can be measured using instruments such as voltmeters and ammeters.

Q: What is the relationship between the electrical force and the electric field?

A: The electrical force is related to the electric field, which is a vector field that describes the distribution of electric charge.

Q: Can the electrical force be used to generate electricity?

A: Yes, the electrical force can be used to generate electricity through the process of electromagnetic induction.

Q: What are some of the applications of the electrical force?

A: Some of the applications of the electrical force include the operation of electrical devices such as motors, generators, and transformers, as well as the transmission of electrical energy over long distances.

Conclusion

In this article, we have addressed some of the frequently asked questions about electrical force. We hope that this information has been helpful in clarifying some of the concepts and principles related to electrical force.

References

  • Coulomb, C.-A. de. (1785). "Sur la force de la répulsion ou d'attraction des corps électrisés." Histoire de l'Académie Royale des Sciences, 361-387.
  • Griffiths, D. J. (2013). Introduction to Electrodynamics. Pearson Education.
  • Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics. John Wiley & Sons.