Calculating the Initial Force

Oct 13, 2025 by recoveryshake.com 76 views

Coulomb's law is a fundamental concept in physics that describes the interaction between charged particles. It 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 explore the application of Coulomb's law to predict the force between two particles separated by a certain distance and then doubled.

Coulomb's Law Equation

The equation for Coulomb's law is given by:

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

where:

$F$ is the force between the two charges in Newtons (N)
$k$ is Coulomb's constant, which is approximately $8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$
$q_1$ and $q_2$ are the charges in Coulombs (C)
$r$ is the distance between the charges in meters (m)

Given Values

We are given two particles with charges of $1.25 \times 10^{-9} \, C$ and $1.92 \times 10^{-9} \, C$ , separated by a distance of $0.38 \, m$ . We want to predict the force between the particles if the distance is doubled.

Calculating the Initial Force

Using the equation for Coulomb's law, we can calculate the initial force between the particles:

F_{\text{initial}} = \frac{k \cdot q_1 \cdot q_2}{r^2}

Substituting the given values, we get:

F_{\text{initial}} = \frac{(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \cdot (1.25 \times 10^{-9} \, \text{C}) \cdot (1.92 \times 10^{-9} \, \text{C})}{(0.38 \, \text{m})^2}

Simplifying the expression, we get:

F_{\text{initial}} = 1.43 \times 10^{-6} \, \text{N}

Calculating the Final Force

If the distance between the particles is doubled, the new distance is $2 \times 0.38 \, m = 0.76 \, m$ . We can use the equation for Coulomb's law to calculate the final force:

F_{\text{final}} = \frac{k \cdot q_1 \cdot q_2}{(2r)^2}

Substituting the given values, we get:

F_{\text{final}} = \frac{(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \cdot (1.25 \times 10^{-9} \, \text{C}) \cdot (1.92 \times 10^{-9} \, \text{C})}{(2 \cdot 0.38 \, \text{m})^2}

Simplifying the expression, we get:

F_{\text{final}} = 5.71 \times 10^{-7} \, \text{N}

Comparing the Initial and Final Forces

We can see that the final force is approximately $40\%$ of the initial force. This makes sense, since the force is inversely proportional to the square of the distance between the charges.

Conclusion

In this article, we used Coulomb's law to predict the force between two particles separated by a certain distance and then doubled. We calculated the initial and final forces and compared them to see how the force changes when the distance is doubled. This demonstrates the application of Coulomb's law in predicting the behavior of charged particles.

References

Coulomb, C. A. (1785). Theorie des Électricités et du Magnétisme. Paris: Imprimerie Royale.
Griffiths, D. J. (2017). Introduction to Electrodynamics. 4th ed. Pearson Education.

Q: What is Coulomb's law?

A: Coulomb's law is a mathematical equation that describes the force between two charged particles. It 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 in Newtons (N)
$k$ is Coulomb's constant, which is approximately $8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$
$q_1$ and $q_2$ are the charges in Coulombs (C)
$r$ is the distance between the charges in meters (m)

Q: What is Coulomb's constant?

A: Coulomb's constant is a fundamental constant in physics that relates the force between two charged particles to their charges and distance. It is approximately $8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$ .

Q: What is the unit of force in Coulomb's law?

A: The unit of force in Coulomb's law is Newtons (N).

Q: What is the unit of charge in Coulomb's law?

A: The unit of charge in Coulomb's law is Coulombs (C).

Q: What is the unit of distance in Coulomb's law?

A: The unit of distance in Coulomb's law is meters (m).

Q: How does the force between two charged particles change with distance?

A: The force between two charged particles decreases with distance. Specifically, it is inversely proportional to the square of the distance between them.

Q: How does the force between two charged particles change with charge?

A: The force between two charged particles increases with charge. Specifically, it is directly proportional to the product of the charges.

Q: Can Coulomb's law be used to predict the force between two charged particles in any situation?

A: Coulomb's law can be used to predict the force between two charged particles in many situations, but it is not applicable in all situations. For example, it is not applicable when the charges are moving at high speeds or when the distance between the charges is very small.

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

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

Predicting the force between charged particles in electrical systems
Understanding the behavior of charged particles in magnetic fields
Designing electrical circuits and devices
Understanding the behavior of charged particles in the universe

Conclusion

Coulomb's law is a fundamental concept in physics that describes the interaction between charged particles. In this article, we have answered some frequently asked questions about Coulomb's law and explored its applications in the real world.