⚡ Coulomb's Law Calculator
Calculate electrostatic force between charges
Use positive for positive charge, negative for negative charge
Distance between the centers of the two charges
How to Use This Calculator
Enter First Charge
Input the magnitude and sign of the first charge in Coulombs. Use positive for positive charges, negative for negative charges. Use scientific notation for small values (e.g., 1e-6 for 1 microcoulomb).
Enter Second Charge
Input the magnitude and sign of the second charge in Coulombs. Like charges (both positive or both negative) will result in repulsive force, opposite charges will result in attractive force.
Enter Distance
Input the distance between the centers of the two charges in meters. This should be the separation distance between the point charges.
Calculate
Click the "Calculate Force" button to get the electrostatic force in Newtons. A positive force indicates repulsion, negative indicates attraction.
Formula
F = k × (q₁ × q₂) / r²
Where:
- F = Electrostatic Force (Newtons, N)
- k = Coulomb's constant = 8.99 × 10⁹ N⋅m²/C²
- q₁ = First charge (Coulombs, C)
- q₂ = Second charge (Coulombs, C)
- r = Distance between charges (meters, m)
Example Calculation:
For two charges of 1 μC (1 × 10⁻⁶ C) each, separated by 1 cm (0.01 m):
F = 8.99 × 10⁹ × (1 × 10⁻⁶) × (1 × 10⁻⁶) / (0.01)²
F = 8.99 × 10⁹ × 1 × 10⁻¹² / 1 × 10⁻⁴
F = 89.9 N
Note: The force is repulsive if charges have the same sign, attractive if they have opposite signs. The force magnitude follows an inverse square law with distance.
About Coulomb's Law Calculator
The Coulomb's Law Calculator determines the electrostatic force between two point charges. Coulomb's law is a fundamental principle in electrostatics that describes how charged particles interact. This calculator is essential for understanding electric forces, field interactions, and electrostatic phenomena in physics and engineering.
When to Use This Calculator
- Physics Education: Solve problems involving electrostatic forces and charge interactions
- Electrostatics Analysis: Calculate forces between charged objects in electrostatic systems
- Particle Physics: Determine forces between charged particles in particle physics experiments
- Electrical Engineering: Analyze charge distributions and electric field effects
- Research: Calculate forces in plasma physics, charged particle beams, and related fields
Why Use Our Calculator?
- ✅ Accurate Calculations: Uses precise Coulomb's constant for exact results
- ✅ Handles All Charge Types: Works with positive and negative charges
- ✅ Scientific Notation: Supports very large and very small charge values
- ✅ Free Tool: No registration or payment required
- ✅ Educational: Visualizes the inverse square law relationship
Common Applications
Electrostatic Precipitators: Calculate forces between charged particles and collector plates in air pollution control systems, where understanding charge interactions is crucial for efficient particle removal.
Particle Accelerators: Analyze forces between charged particles in accelerators, helping engineers design particle beam focusing and steering systems based on Coulomb interactions.
Atomic Physics: Understand forces in atomic systems, where electrons experience Coulomb forces from the nucleus, fundamental to understanding atomic structure and chemical bonding.
Tips for Best Results
- Remember: like charges repel (positive-positive or negative-negative), opposite charges attract
- The force follows an inverse square law - doubling distance reduces force by a factor of 4
- Use consistent units: charges in Coulombs, distance in meters, force in Newtons
- For point charges, use the distance between their centers
- Coulomb's constant k ≈ 8.99 × 10⁹ N⋅m²/C² is approximately 9 × 10⁹ for rough estimates
Frequently Asked Questions
What does a negative force mean?
A negative force indicates an attractive force between opposite charges. A positive force indicates a repulsive force between like charges. The sign of the force depends on the product of the two charges.
Does Coulomb's law work for all charge distributions?
Coulomb's law applies exactly to point charges. For extended charge distributions, you need to integrate over the charge distribution. For spherically symmetric distributions, you can treat them as point charges at the center if you're outside the sphere.
What is the value of Coulomb's constant?
Coulomb's constant k = 8.99 × 10⁹ N⋅m²/C² (approximately 9 × 10⁹). It's related to the permittivity of free space: k = 1/(4πε₀), where ε₀ = 8.85 × 10⁻¹² C²/(N⋅m²).
How does distance affect the force?
The force follows an inverse square law with distance. If you double the distance, the force becomes 1/4 of the original. If you triple the distance, the force becomes 1/9 of the original. This is similar to the gravitational force law.
Can I use this for charges in a medium?
This calculator uses the formula for charges in vacuum or air. For charges in a dielectric medium, you need to divide by the relative permittivity (dielectric constant) of the medium: F = k(q₁q₂)/(εᵣr²).
What units should I use for charges?
Use Coulombs (C) for charges. Common conversions: 1 microcoulomb (μC) = 1 × 10⁻⁶ C, 1 nanocoulomb (nC) = 1 × 10⁻⁹ C. An electron has charge -1.602 × 10⁻¹⁹ C.