A Negative Charge Of \[$-2 \, \text{C}\$\] And A Positive Charge Of \[$3 \, \text{C}\$\] Are Separated By \[$80 \, \text{m}\$\]. What Is The Force Between The Two Charges?

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Introduction

When two charges are present in a system, they interact with each other through the electromagnetic force. The force between two charges can be calculated using Coulomb's Law, which states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In this article, we will use Coulomb's Law to calculate the force between a negative charge of {-2 , \text{C}$}$ and a positive charge of ${3 \, \text{C}\$} that are separated by ${80 \, \text{m}\$}.

Coulomb's Law

Coulomb's Law is a fundamental concept in physics that describes the interaction between two charges. The law states that the force between two point charges is given by the equation:

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

where:

• $F$ is the force between the two charges
• $k$ is Coulomb's constant, which is approximately ${9 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2}\$}
• $q_1$ and $q_2$ are the magnitudes of the two charges
• $r$ is the distance between the two charges

Calculating the Force

To calculate the force between the two charges, we can plug in the values given in the problem into the equation for Coulomb's Law:

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

$$F = \frac{(9 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2}) \cdot (-2 \, \text{C}) \cdot (3 \, \text{C})}{(80 \, \text{m})^2}$$

$$F = \frac{(-54 \times 10^9 \, \text{N} \cdot \text{m}^2)}{(6400 \, \text{m}^2)}$$

$$F = -8.4375 \times 10^6 \, \text{N}$$

Conclusion

In this article, we used Coulomb's Law to calculate the force between a negative charge of {-2 , \text{C}$}$ and a positive charge of ${3 \, \text{C}\$} that are separated by ${80 \, \text{m}\$}. The force between the two charges was calculated to be {-8.4375 \times 10^6 , \text{N}$}$. This result shows that the force between the two charges is attractive, as the negative charge is repelled by the positive charge.

Applications of Coulomb's Law

Coulomb's Law has many practical applications in physics and engineering. Some examples include:

• Electric motors: Coulomb's Law is used to calculate the force between the rotor and stator of an electric motor.
• Electric generators: Coulomb's Law is used to calculate the force between the rotor and stator of an electric generator.
• Particle accelerators: Coulomb's Law is used to calculate the force between charged particles in a particle accelerator.
• Semiconductor devices: Coulomb's Law is used to calculate the force between charged particles in a semiconductor device.

Limitations of Coulomb's Law

While Coulomb's Law is a powerful tool for calculating the force between two charges, it has some limitations. Some of these limitations include:

• Point charges: Coulomb's Law assumes that the charges are point charges, which is not always the case in real-world systems.
• Non-uniform charge distribution: Coulomb's Law assumes that the charge distribution is uniform, which is not always the case in real-world systems.
• Relativistic effects: Coulomb's Law assumes that the charges are moving at non-relativistic speeds, which is not always the case in real-world systems.

Future Research Directions

There are many areas of research that are related to Coulomb's Law. Some of these areas include:

• Quantum mechanics: Researchers are working to develop a quantum mechanical theory of electromagnetism that can be used to calculate the force between charged particles.
• Relativistic electromagnetism: Researchers are working to develop a relativistic theory of electromagnetism that can be used to calculate the force between charged particles.
• Plasma physics: Researchers are working to develop a theory of plasma physics that can be used to calculate the force between charged particles in a plasma.

Conclusion

In conclusion, Coulomb's Law is a fundamental concept in physics that describes the interaction between two charges. The law has many practical applications in physics and engineering, but it also has some limitations. Researchers are working to develop new theories and models that can be used to calculate the force between charged particles in a variety of situations.

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Q&A

Q: What is Coulomb's Law?

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

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

A: The equation for Coulomb's Law is:

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

where:

• $F$ is the force between the two charges
• $k$ is Coulomb's constant, which is approximately ${9 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2}\$}
• $q_1$ and $q_2$ are the magnitudes of the two charges
• $r$ is the distance between the two charges

Q: What is the force between a negative charge of {-2 , \text{C}$}$ and a positive charge of ${3 \, \text{C}\$} that are separated by ${80 \, \text{m}\$}?

A: To calculate the force between the two charges, we can plug in the values given in the problem into the equation for Coulomb's Law:

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

$$F = \frac{(9 \times 10^9 \, \text{N} \cdot \text{m}^2 \cdot \text{C}^{-2}) \cdot (-2 \, \text{C}) \cdot (3 \, \text{C})}{(80 \, \text{m})^2}$$

$$F = \frac{(-54 \times 10^9 \, \text{N} \cdot \text{m}^2)}{(6400 \, \text{m}^2)}$$

$$F = -8.4375 \times 10^6 \, \text{N}$$

Q: Is the force between the two charges attractive or repulsive?

A: The force between the two charges is attractive, as the negative charge is repelled by the positive charge.

Q: What are some practical applications of Coulomb's Law?

A: Some practical applications of Coulomb's Law include:

• Electric motors: Coulomb's Law is used to calculate the force between the rotor and stator of an electric motor.
• Electric generators: Coulomb's Law is used to calculate the force between the rotor and stator of an electric generator.
• Particle accelerators: Coulomb's Law is used to calculate the force between charged particles in a particle accelerator.
• Semiconductor devices: Coulomb's Law is used to calculate the force between charged particles in a semiconductor device.

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

A: Some limitations of Coulomb's Law include:

• Point charges: Coulomb's Law assumes that the charges are point charges, which is not always the case in real-world systems.
• Non-uniform charge distribution: Coulomb's Law assumes that the charge distribution is uniform, which is not always the case in real-world systems.
• Relativistic effects: Coulomb's Law assumes that the charges are moving at non-relativistic speeds, which is not always the case in real-world systems.

Q: What are some areas of research related to Coulomb's Law?

A: Some areas of research related to Coulomb's Law include:

• Quantum mechanics: Researchers are working to develop a quantum mechanical theory of electromagnetism that can be used to calculate the force between charged particles.
• Relativistic electromagnetism: Researchers are working to develop a relativistic theory of electromagnetism that can be used to calculate the force between charged particles.
• Plasma physics: Researchers are working to develop a theory of plasma physics that can be used to calculate the force between charged particles in a plasma.

Q: What is the significance of Coulomb's Law in physics and engineering?

A: Coulomb's Law is a fundamental concept in physics and engineering that describes the interaction between two charges. The law has many practical applications in physics and engineering, and it is used to calculate the force between charged particles in a variety of situations.