Understanding the Force Between Negative Charges: A DEEP Dive into Coulomb’s Law

When working with electrostatics, understanding the forces between charges is fundamental. This article explores the calculation of the force between two negative charges, given specific parameters, and delves into the mathematical principles behind it. We will also discuss the importance of the Inverse-Square Law in such scenarios.

Given Parameters and Initial Conditions

The problem presented states that two negative charges are 2 meters apart and repel each other with a force of 2 Newtons. This scenario aligns with Coulomb's Law, which describes the magnitude of the electrostatic force between two point charges.

Coulomb's Law

Coulomb's Law is expressed by the following equation:

F k frac{q_1 q_2}{r^2}

where F is the magnitude of the electrostatic force between the charges, k is Coulomb's constant (approximately 8.99 x 109 N·m2/C2), q_1 and q_2 are the magnitudes of the charges, and r is the distance between the charges.

Given:

F 2 N r 2 m Both charges are negative but of equal magnitudes, hence q_1 q_2 q

Plugging these values into Coulomb's Law, we get:

2 8.99 times 10^9 frac{q^2}{2^2}

Let's solve for q by rearranging the equation:

frac{2}{8.99 times 10^9} frac{q^2}{4}

frac{8}{8.99 times 10^9} q^2

q sqrt{frac{8}{8.99 times 10^9}} approx 3.2 times 10^{-5}, C

The Inverse-Square Law

The Inverse-Square Law states that the magnitude of the force between two objects decreases by the square of the distance between them. This is a critical principle in electrostatics and physics in general, applicable to various fields like astronomy and electromagnetism.

Given that the distance doubles from 2 meters to 4 meters:

4 2^2

Therefore, the force between the charges should be:

frac{2}{(2)^2} 0.5 , N

This aligns with the Inverse-Square Law, where the force F is inversely proportional to the square of the distance r.

Conclusion

Understanding the forces between charges involves comprehending both Coulomb's Law and the Inverse-Square Law. By applying these principles, we can solve complex problems involving electrostatic forces. The calculation of the force between two negative charges provides a clear demonstration of how these laws operate in real-world scenarios.

References

1. Coulomb’s Law - HyperPhysics 2. Inverse-Square Law - Wikipedia 3. Electrostatics - University of Texas