Coulomb's Law Calculator

Category: Physics
- March 20, 2025
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Coulomb's Law describes the electrostatic force between two charged particles. This fundamental principle of electrostatics states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

This calculator allows you to determine the electrostatic force, electric field, and potential energy between charged particles using Coulomb's Law.

What would you like to calculate?

C
? The magnitude of the first charge in Coulombs (C). For example, an electron has a charge of -1.602 × 10⁻¹⁹ C.
C
? The magnitude of the second charge in Coulombs (C).
? The distance between the centers of the two charges.

Display Options

? Include the effect of a dielectric medium between the charges. This will reduce the electrostatic force by a factor of the dielectric constant.

About Coulomb's Law

Coulomb's Law, formulated by French physicist Charles-Augustin de Coulomb in 1785, describes the electrostatic force between two electrically charged particles. It is a fundamental principle in electrostatics.

The Mathematical Expression:

Coulomb's Law is mathematically expressed as:

F = k × (|q₁ × q₂|) / r²

Where:

  • F is the electrostatic force between the charges (in Newtons, N)
  • k is Coulomb's constant (8.9875 × 10⁹ N·m²/C²)
  • q₁ and q₂ are the magnitudes of the charges (in Coulombs, C)
  • r is the distance between the centers of the charges (in meters, m)
Related Electric Field Equations:

The electric field at a distance r from a point charge q is given by:

E = k × |q| / r²

The electric potential at a distance r from a point charge q is given by:

V = k × q / r

The electric potential energy of two point charges q₁ and q₂ separated by a distance r is given by:

U = k × q₁ × q₂ / r
Effect of Dielectric Media:

When charges are in a medium other than vacuum, the electrostatic force is reduced by a factor equal to the dielectric constant (ε) of the medium:

F = k × (|q₁ × q₂|) / (ε × r²)

The dielectric constant is a measure of the medium's ability to "store" electric field energy. The higher the dielectric constant, the more the medium weakens the electric field.

Medium Dielectric Constant (ε)
Vacuum 1.0 (exact)
Air (at STP) 1.00059
Water 80
Glass 5-10
Plastic 2-4
Paper 3.7
Oil 2.4
Key Applications:
  • Atomic and Molecular Structure: Coulomb's Law explains the attractive force between electrons and the nucleus in atoms.
  • Electrical Engineering: Used in designing capacitors, insulators, and other electrical components.
  • Chemical Bonding: Ionic bonds and electrostatic interactions in molecules are described by Coulomb's Law.
  • Electrostatic Precipitators: Used to remove particles from a gas stream by applying an electric charge.
  • Lightning: The buildup and discharge of electric charge in clouds can be explained using Coulomb's Law.
  • Biological Processes: Many biological processes involve electrostatic interactions between charged molecules.

What is Coulomb's Law Calculator?

The Coulomb's Law Calculator is a tool designed to help users calculate the electrostatic force, electric field, electric potential, and potential energy between charged particles. Based on Coulomb's Law, this tool simplifies calculations that are fundamental in physics, electrical engineering, and chemistry.

Coulomb's Law Formula

Coulomb's Law is mathematically expressed as:

F = k × (|q₁ × q₂|) / r²

Where:

  • F is the electrostatic force (in Newtons, N).
  • k is Coulomb’s constant (8.9875 × 10⁹ N·m²/C²).
  • q₁ and q₂ are the magnitudes of the charges (in Coulombs, C).
  • r is the distance between the centers of the two charges (in meters, m).

How to Use the Calculator

The calculator allows users to compute four different values based on Coulomb’s Law:

  • Electrostatic Force – Determines the force between two charges.
  • Electric Field – Calculates the field strength at a given point.
  • Electric Potential – Computes the potential at a certain distance.
  • Potential Energy – Evaluates the stored energy between charges.

Steps to Use the Calculator

  1. Select what you want to calculate (Force, Field, Potential, or Energy).
  2. Enter the required values such as charge magnitude and distance.
  3. Choose the unit for distance (meters, centimeters, etc.).
  4. Adjust display preferences (decimal places, scientific notation, etc.).
  5. Click "Calculate" to view the results.

Why Use This Calculator?

This tool is useful for students, engineers, and professionals who need quick and accurate electrostatic calculations. It helps in:

  • Understanding basic electrostatic interactions in physics.
  • Solving problems related to charged particles in chemistry.
  • Analyzing electrical forces in circuits and materials.

FAQ

What is Coulomb's Law used for?

Coulomb's Law is used to calculate the force between charged particles. It helps in understanding electrical interactions in various scientific and engineering applications.

Can this calculator handle different units?

Yes, you can choose different units for distance (meters, centimeters, millimeters, etc.) to match your needs.

Does the calculator consider the medium between charges?

Yes, there is an option to include a dielectric constant, which accounts for the effect of the medium on the electrostatic force.

What happens if I enter a negative charge?

Negative values indicate negatively charged particles, such as electrons. The calculator automatically determines whether the force is attractive or repulsive based on the sign of the charges.

Conclusion

The Coulomb's Law Calculator is a powerful and easy-to-use tool for calculating electrostatic properties. Whether you are studying physics, working on engineering problems, or analyzing electrical forces, this tool provides accurate results quickly.