Coulomb’s Law


The fundamental law defining the electrostatic force between charged objects.

Introduction

Coulomb’s Law is a cornerstone of electrostatics and plays a vital role in our understanding of electrical interactions. It explains how the force between two charged particles depends on the magnitude of the charges and the distance between them. Whether you are studying physics, engineering, or chemistry, a thorough grasp of Coulomb’s Law is essential.

Variables & Units

The core formula of Coulomb’s Law is F = k × |q₁ × q₂| / r², where:

  • F (Force): The electrostatic force between the charges, measured in newtons (N).
  • q₁ and q₂ (Charges): The magnitudes of the two point charges, measured in coulombs (C).
  • r (Distance): The distance between the centers of the two charges, measured in meters (m).
  • k (Coulomb’s Constant): Approximately 8.99×10⁹ N·m²/C².

Using consistent SI units is essential for accurate calculations.

The Fundamental Equation

Coulomb’s Law is mathematically expressed as:

F = k × |q₁ × q₂| / r²

This equation can be rearranged to solve for other variables. For example:

  • To calculate a charge (q₂): q₂ = F × r² / (k × |q₁|)
  • To calculate the distance (r): r = √(k × |q₁ × q₂| / F)

How to Use Coulomb’s Law

Applying Coulomb’s Law is straightforward. Follow these steps:

  1. Identify the Known Values: Determine the magnitudes of the charges (q₁ and q₂) and the distance (r) between them.
  2. Select the Correct Formula: Use F = k × |q₁ × q₂| / r² to calculate the electrostatic force, or rearrange the formula to solve for an unknown variable.
  3. Substitute and Solve: Make sure all values are in SI units, substitute them into the equation, and solve for the unknown.

Example Problems

Example 1: Calculating Force

Problem: Two point charges of 3 μC and 4 μC are placed 0.2 m apart. What is the force between them? (Note: 1 μC = 1×10⁻⁶ C)

F = 8.99×10⁹ × |(3×10⁻⁶ C × 4×10⁻⁶ C)| / (0.2 m)²
F = 8.99×10⁹ × (12×10⁻¹²) / 0.04
F ≈ 8.99×10⁹ × 3×10⁻¹¹ = 2.70 N

Explanation: The electrostatic force between the two charges is approximately 2.70 newtons.

Example 2: Calculating a Charge

Problem: If two charges exert a force of 0.05 N on each other when separated by 0.5 m, and one charge is 2 μC, what is the other charge?

q₂ = (F × r²) / (k × q₁)
q₂ = (0.05 N × (0.5 m)²) / (8.99×10⁹ N·m²/C² × 2×10⁻⁶ C)
q₂ ≈ (0.05 × 0.25) / (8.99×10⁹ × 2×10⁻⁶)
q₂ ≈ 0.0125 / 17,980 ≈ 6.95×10⁻⁷ C

Explanation: The unknown charge is approximately 0.695 μC.

Example 3: Calculating Distance

Problem: Two charges of 5 μC each exert a force of 0.2 N on each other. What is the distance between them?

r = √(k × |q₁ × q₂| / F)
r = √(8.99×10⁹ × (5×10⁻⁶ C × 5×10⁻⁶ C) / 0.2 N)
r = √(8.99×10⁹ × 25×10⁻¹² / 0.2)
r = √(224.75×10⁻³ / 0.2)
r = √(1.12375) ≈ 1.06 m

Explanation: The distance between the charges is approximately 1.06 meters.

Practical Applications

Coulomb’s Law is crucial in many fields, such as:

  • Electrostatics: Understanding the forces between charged particles in atoms and molecules.
  • Capacitor Design: Predicting how charges interact in electrical components.
  • Particle Accelerators: Calculating repulsive forces between charged particles.
  • Electrical Engineering: Designing sensors and devices that rely on electrostatic forces.

Advanced Concepts

Beyond basic calculations, Coulomb’s Law leads to deeper topics:

  • Electric Fields: Coulomb’s Law forms the basis for defining the electric field generated by point charges.
  • Force Superposition: In systems with multiple charges, the net force is the vector sum of individual forces.
  • Medium Effects: In materials other than vacuum, the law is modified by the dielectric constant of the medium.

Frequently Asked Questions

What is Coulomb’s Law?

It is a principle in electrostatics stating that the magnitude of the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

What is the formula for Coulomb’s Law?

The formula is F = k × |q₁ × q₂| / r², where k is Coulomb’s constant.

What units are used in Coulomb’s Law?

Force is measured in newtons (N), charge in coulombs (C), distance in meters (m), and k is expressed in N·m²/C².

How do I solve problems using Coulomb’s Law?

Identify the known values (charges and distance), substitute them into the formula, and solve for the unknown variable. You can also rearrange the equation to determine a missing charge or distance.

Conclusion

Coulomb’s Law is a fundamental tool in understanding electrostatic interactions. Mastering this law provides critical insight into how charged particles interact, laying the groundwork for advanced studies in electromagnetism and practical applications in science and engineering.

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