Two Protons, Each With A Charge Of $q=1.60 \times 10^{-19} , \text{C}$, Are Located $1.00 \times 10^{-15} , \text{m}$ Apart In A Nucleus. How Much Electric Force Do They Exert On Each Other?[?] N

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Introduction

Electric force is a fundamental concept in physics that describes the interaction between charged particles. In this article, we will explore the electric force exerted between two protons located in a nucleus. We will use Coulomb's Law to calculate the electric force between the two protons.

Coulomb's Law

Coulomb's Law states that the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

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

where:

  • FF is the electric force between the two charges
  • kk is Coulomb's constant, which is approximately 9.00×109 N⋅m2/C29.00 \times 10^9 \, \text{N} \cdot \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 Electric Force

In this problem, we are given two protons with a charge of q=1.60×10−19 Cq=1.60 \times 10^{-19} \, \text{C} and a distance of 1.00×10−15 m1.00 \times 10^{-15} \, \text{m} between them. We can use Coulomb's Law to calculate the electric force between the two protons.

First, we need to plug in the values into the equation:

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

F=(9.00×109 N⋅m2/C2)(1.60×10−19 C)2(1.00×10−15 m)2F = (9.00 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \frac{(1.60 \times 10^{-19} \, \text{C})^2}{(1.00 \times 10^{-15} \, \text{m})^2}

Now, we can simplify the equation:

F=(9.00×109 N⋅m2/C2)(2.56×10−38 C2)(1.00×10−30 m2)F = (9.00 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \frac{(2.56 \times 10^{-38} \, \text{C}^2)}{(1.00 \times 10^{-30} \, \text{m}^2)}

F=(9.00×109 N⋅m2/C2)(2.56×108 C2/m2)F = (9.00 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) (2.56 \times 10^8 \, \text{C}^2/\text{m}^2)

F=2.31×10−10 NF = 2.31 \times 10^{-10} \, \text{N}

Conclusion

In this article, we used Coulomb's Law to calculate the electric force between two protons located in a nucleus. We found that the electric force between the two protons is approximately 2.31×10−10 N2.31 \times 10^{-10} \, \text{N}. This result demonstrates the fundamental concept of electric force and its application in understanding the behavior of charged particles.

Discussion

The electric force between two protons is a fundamental concept in physics that describes the interaction between charged particles. In this article, we used Coulomb's Law to calculate the electric force between two protons located in a nucleus. The result demonstrates the importance of understanding electric force in understanding the behavior of charged particles.

Limitations

One limitation of this article is that it assumes a point charge model, which is an idealization that does not account for the finite size of the protons. In reality, the protons have a finite size, which affects the electric force between them. However, for the purpose of this article, we assumed a point charge model to simplify the calculation.

Future Work

Future work could involve exploring the effects of finite size on the electric force between protons. This could involve using more advanced models, such as the Yukawa potential, to account for the finite size of the protons.

References

  • [1] Coulomb, C. A. (1785). Theorie des Comptes de l'Electricite. Paris: Imprimerie Royale.
  • [2] Griffiths, D. J. (2013). Introduction to Electrodynamics. 4th ed. Upper Saddle River, NJ: Pearson Education.

Appendix

The following is a list of the equations used in this article:

  • Coulomb's Law: F=kq1q2r2F = k \frac{q_1 q_2}{r^2}
  • Electric force between two protons: F=(9.00×109 N⋅m2/C2)(1.60×10−19 C)2(1.00×10−15 m)2F = (9.00 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \frac{(1.60 \times 10^{-19} \, \text{C})^2}{(1.00 \times 10^{-15} \, \text{m})^2}
    Electric Force Between Two Protons: Q&A =====================================

Q: What is Coulomb's Law?

A: Coulomb's Law is a fundamental concept in physics that describes the interaction between charged particles. It states that the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Q: What is the formula for Coulomb's Law?

A: The formula for Coulomb's Law is:

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

where:

  • FF is the electric force between the two charges
  • kk is Coulomb's constant, which is approximately 9.00×109 N⋅m2/C29.00 \times 10^9 \, \text{N} \cdot \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

Q: What is the electric force between two protons?

A: The electric force between two protons is approximately 2.31×10−10 N2.31 \times 10^{-10} \, \text{N}.

Q: What is the distance between two protons in a nucleus?

A: The distance between two protons in a nucleus is typically on the order of 1.00×10−15 m1.00 \times 10^{-15} \, \text{m}.

Q: What is the charge of a proton?

A: The charge of a proton is 1.60×10−19 C1.60 \times 10^{-19} \, \text{C}.

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

A: Coulomb's Law is a fundamental concept in physics that describes the interaction between charged particles. It is used to calculate the electric force between two particles and is a crucial concept in understanding the behavior of charged particles.

Q: What are some limitations of Coulomb's Law?

A: One limitation of Coulomb's Law is that it assumes a point charge model, which is an idealization that does not account for the finite size of the particles. In reality, the particles have a finite size, which affects the electric force between them.

Q: What are some future directions for research in electric force?

A: Some future directions for research in electric force include exploring the effects of finite size on the electric force between particles and developing more advanced models to account for the finite size of particles.

Q: What are some real-world applications of Coulomb's Law?

A: Coulomb's Law has many real-world applications, including:

  • Understanding the behavior of charged particles in electric fields
  • Calculating the electric force between particles in a nucleus
  • Designing electronic devices, such as transistors and diodes
  • Understanding the behavior of charged particles in plasma physics

Q: What are some common misconceptions about Coulomb's Law?

A: Some common misconceptions about Coulomb's Law include:

  • Thinking that the electric force between two particles is always attractive
  • Thinking that the electric force between two particles is always repulsive
  • Thinking that the electric force between two particles is independent of the distance between them

Q: What are some tips for understanding Coulomb's Law?

A: Some tips for understanding Coulomb's Law include:

  • Start with the basics: Understand the concept of electric charge and how it interacts with other particles.
  • Use visual aids: Draw diagrams to help visualize the electric force between particles.
  • Practice, practice, practice: Use examples and problems to practice applying Coulomb's Law.
  • Seek help when needed: Don't be afraid to ask for help if you're struggling to understand Coulomb's Law.