Calculating the Distance Between Two Negative Charges Using Coulomb’s Law

In this article, we will explore a practical problem involving Coulomb's Law, which is a fundamental principle in electrostatics. We will calculate the distance between two negative charges, specifically -2 nC and -5 nC, such that they repel each other with a force of 10 N.

Understanding Coulomb's Law

Coulomb's Law describes the electrostatic force between two point charges. The law is expressed as:

F kq1q2/d^2

where:

F is the electrostatic force between the charges (in Newtons, N). k is Coulomb's constant (approximately 9×10^9 N·m^2/C^2). q1 and q2 are the magnitudes of the two charges (in Coulombs, C). d is the distance between the charges (in meters, m).

Solving for the Distance Between Charges

Given the following details, we will calculate the required distance:

Charge 1: -2 nC (or -2×10^-9 C) Charge 2: -5 nC (or -5×10^-9 C) Repulsive force: 10 N

Plugging these values into the equation F kq1q2/d^2, we get:

Fd^2 kq1q2

Given:

F 10 N k ≈ 9×10^9 N·m^2/C^2 q1 -2×10^-9 C q2 -5×10^-9 C

Substituting these values into the equation:

10d^2 9×10^9 × (-2×10^-9) × (-5×10^-9)

10d^2 90×10^-19

d^2 90×10^-9 m^2

d √(90×10^-9 m^2)

d 9.49×10^-5 m

Therefore, the distance between the two negative charges is approximately 94.9 micrometers (μm).

Key Takeaways

Coulomb's Law is a powerful tool for understanding the electrostatic forces between charges. Correctly handling units, such as changing nanocoulombs (nC) to coulombs (C), is crucial. Algebra plays a key role in solving complex physics problems.

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