Coulomb's Law — Electrostatic Force Between Charges
Coulomb's Law describes the electrostatic force between two point charges: F = k|q₁q₂|/r². Like charges repel, opposite charges attract. The force is proportional to the product of charges and inversely proportional to distance squared. Coulomb constant k = 8.99×10⁹ N·m²/C².
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Force is proportional to charge product and inversely proportional to r² Like charges repel (F > 0); opposite charges attract (F < 0) Electric field E = F/q for a test charge Potential energy U = kq₁q₂/r for two-charge system
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Why: Coulomb's Law is fundamental to electrostatics and explains how charged particles interact. It applies to atomic structure, electric circuits, and electromagnetic phenomena. Dielectric media reduce the force by the relative permittivity.
How: Enter two charges and their separation distance. Select units and dielectric medium. The calculator computes force, electric field at each charge, and potential energy. Supports multiple unit systems.
Run the calculator when you are ready.
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For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Electrostatic force between two protons 1 fm apart is ~230 N — 10³⁶× stronger than gravity
— HyperPhysics
Coulomb discovered his law in 1785 using a torsion balance
— Physics Classroom
Coulomb constant k = 1/(4πε₀) in SI units
— NIST
Dielectric media reduce force by relative permittivity εr
— Physics Classroom
📋 Key Takeaways
- • Coulomb's Law describes the electrostatic force between two point charges
- • Force is proportional to the product of charges and inversely proportional to distance squared
- • Like charges repel, opposite charges attract
- • Coulomb constant: k = 8.99×10⁹ N·m²/C²
- • Force is reduced in dielectric media by the relative permittivity (εᵣ)
💡 Did You Know?
📖 How Coulomb's Law Works
Coulomb's Law provides a mathematical description of the electrostatic force between two point charges. The force is proportional to the product of the charge magnitudes and inversely proportional to the square of their separation distance.
The Inverse Square Law
F = k × |q₁q₂| / r²
Doubling the distance reduces the force by a factor of 4. This is the same relationship as gravity and light intensity.
Force Direction
Like charges (both positive or both negative) repel each other. Opposite charges attract. The force acts along the line connecting the charges.
🎯 Expert Tips for Electrostatic Calculations
💡 Use Absolute Values for Magnitude
Force magnitude uses |q₁q₂|. The sign of charges determines direction (attractive vs repulsive), not magnitude.
💡 Consider Medium Permittivity
Forces in water, glass, or other dielectrics are reduced by relative permittivity. Water reduces force by 80×!
💡 Superposition for Multiple Charges
For multiple charges, calculate force from each charge separately, then add vectorially. This is the superposition principle.
💡 Check Units Carefully
Always convert to SI units: charges in Coulombs, distance in meters. The calculator handles unit conversions automatically.
⚖️ Electrostatic Force vs Other Forces
| Force Type | Formula | Range | Notes |
|---|---|---|---|
| Electrostatic | F = k×|q₁q₂|/r² | Infinite | Inverse square law |
| Gravitational | F = G×m₁m₂/r² | Infinite | Much weaker than electrostatic |
| Nuclear Strong | Short range | ~1 fm | Holds nuclei together |
| Magnetic | Depends on motion | Infinite | Only affects moving charges |
❓ Frequently Asked Questions
What is the difference between Coulomb's Law and Newton's Law of Gravitation?
Both follow inverse square laws, but Coulomb's Law describes electrostatic forces between charges, while Newton's Law describes gravitational forces between masses. Electrostatic forces can be attractive or repulsive, while gravity is always attractive. Electrostatic forces are much stronger - about 10³⁶ times stronger for fundamental particles.
Why does distance appear squared in Coulomb's Law?
The inverse square law (r² in denominator) occurs because the electric field spreads out in three-dimensional space. As distance doubles, the field spreads over 4× the area, so force decreases by a factor of 4. This is fundamental to how fields propagate in 3D space.
What happens when charges are very close together?
As distance approaches zero, the force approaches infinity. However, real charges have finite size, and quantum effects become important at atomic scales. Coulomb's Law applies to point charges - idealized charges with no size.
How does a dielectric medium affect the force?
Dielectric materials reduce electrostatic forces by a factor equal to their relative permittivity (εᵣ). Water (εᵣ = 80.1) reduces forces by 80×. This is because the dielectric polarizes, creating an opposing field that partially cancels the original field.
Can Coulomb's Law be used for moving charges?
Coulomb's Law applies to static charges. For moving charges, additional magnetic forces come into play (Lorentz force). However, if charges move slowly, Coulomb's Law still provides a good approximation.
What is the relationship between force, electric field, and potential energy?
Electric field (E) is force per unit charge: E = F/q. Potential energy (U) is the work needed to bring charges together: U = k×q₁q₂/r. Force is the negative gradient of potential energy: F = -dU/dr.
How accurate is Coulomb's Law?
Coulomb's Law is extremely accurate for macroscopic charges and distances. At atomic scales, quantum mechanics modifies the behavior, but Coulomb's Law still applies. It's one of the most precisely verified laws in physics.
What are some real-world applications of Coulomb's Law?
Applications include: capacitor design, atomic structure (electron-proton attraction), particle accelerators, electrostatic precipitators, photocopiers, and understanding chemical bonding. It's fundamental to all electrical phenomena.
📊 Electrostatics by the Numbers
📚 Official Data Sources
⚠️ Disclaimer: This calculator provides estimates based on Coulomb's Law for point charges in ideal conditions. Real-world applications may involve charge distributions, quantum effects at atomic scales, relativistic effects at high speeds, and other factors. Always verify results with experimental data or more sophisticated models for critical applications.
What is Coulomb's Law?
Coulomb's Law describes the electrostatic force between two point charges. Discovered by Charles-Augustin de Coulomb in 1785, it states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. This fundamental law governs all electrostatic interactions and is essential for understanding electricity, atomic physics, and electromagnetic phenomena.
Electrostatic Force
Calculate the magnitude and direction of force between two point charges using the inverse square law.
Key Features:
- Force magnitude calculation
- Attractive vs repulsive forces
- Inverse square law visualization
Electric Field Analysis
Determine the electric field strength at any point due to point charges, essential for understanding field lines and potential.
Calculations:
- Field magnitude at charge locations
- Field direction visualization
- Superposition of fields
Potential Energy
Calculate the electrostatic potential energy stored in the charge configuration, crucial for understanding work and energy in electrostatics.
Applications:
- Energy storage systems
- Atomic binding energy
- Work calculations
How Does Coulomb's Law Work?
Coulomb's Law provides a mathematical description of the electrostatic force between two point charges. The force is proportional to the product of the charge magnitudes and inversely proportional to the square of their separation distance. The direction depends on whether the charges are like (repulsive) or opposite (attractive).
🔬 Scientific Methodology
Calculation Process
- 1Input charge magnitudes and separation distance
- 2Apply Coulomb's Law: F = k × |q₁q₂| / r²
- 3Calculate electric field and potential energy
- 4Account for medium permittivity effects
Why This Approach Works
- Based on fundamental electrostatic principles
- Accounts for inverse square law behavior
- Includes medium permittivity effects
- Provides comprehensive force, field, and energy analysis
When to Use Coulomb's Law Calculator
Coulomb's Law is fundamental to understanding electrostatic interactions in physics, chemistry, and engineering. Use this calculator for analyzing point charge interactions, designing electrical systems, understanding atomic structure, and solving electrostatics problems.
Atomic Physics
Analyze electron-proton interactions, atomic binding forces, and nuclear electrostatic repulsion.
Applications:
- Hydrogen atom structure
- Nuclear force calculations
- Ion interactions
Electrical Engineering
Design capacitors, analyze charge distributions, and calculate forces in electrical systems.
Use Cases:
- Capacitor design
- Charge distribution
- Electrostatic devices
Education & Learning
Understand fundamental electrostatic principles through interactive calculations and visualizations.
Learning Goals:
- Inverse square law
- Force direction
- Medium effects
Coulomb's Law Formulas Explained
Understanding the mathematical relationships in Coulomb's Law is essential for solving electrostatic problems. The formulas below describe the fundamental relationships between charges, distance, force, electric field, and potential energy.
📊 Core Calculation Formulas
Coulomb's Law
Where k = 8.99×10⁹ N·m²/C² is the Coulomb constant, q₁ and q₂ are charge magnitudes, and r is separation distance
Electric Field from Point Charge
Electric field magnitude at distance r from a point charge q
Electrostatic Potential Energy
Potential energy stored in the charge configuration (note: sign depends on charge signs)
Medium Permittivity Effect
Force is reduced by relative permittivity εᵣ in dielectric media (water, glass, etc.)
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