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Coulomb's Law Calculator

Calculate the electrostatic force between charged particles

1.000 μC
-1.000 μC
10.0 cm
Dielectric constant: 1

Enter charge values and distance to calculate electrostatic force

About Coulomb's Law Calculator

About Coulomb's Law Calculator

Understanding electrostatic forces and their fundamental role in electromagnetism

⚡ What is Coulomb's Law?

Coulomb's Law is a fundamental principle in physics that describes the electrostatic force between two charged particles. It was discovered by French physicist Charles-Augustin de Coulomb in the 1780s and is one of the most important laws in electromagnetism.

The Mathematical Statement

F = k|q₁q₂|/r²

Where F is the electrostatic force, k is Coulomb's constant (8.99×10⁹ N⋅m²/C²), q₁ and q₂ are the charges, and r is the distance between them

This law tells us that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It follows an inverse square law, similar to Newton's law of gravitation.

🔑 Key Concepts

Charge Types

There are two types of electric charge: positive and negative. Like charges repel each other, while opposite charges attract each other.

Rule: Positive + Positive = Repulsion, Negative + Negative = Repulsion, Positive + Negative = Attraction

Inverse Square Law

The force decreases with the square of the distance. If you double the distance, the force becomes one-fourth as strong.

Example: At 2m distance, force = F/4; at 3m distance, force = F/9

Coulomb's Constant

The constant k = 8.99×10⁹ N⋅m²/C² relates the units and ensures the law works in the SI system of units.

Units: k has units of N⋅m²/C² to make the equation dimensionally correct

Superposition Principle

When multiple charges are present, the total force on any charge is the vector sum of the individual forces from each other charge.

Vector Addition: Forces add as vectors, considering both magnitude and direction

🔋 Electric Charge and Units

Charge Units

  • Coulomb (C): The SI unit of electric charge
  • Elementary Charge (e): 1.602×10⁻¹⁹ C, the charge of a proton or electron
  • Microcoulomb (μC): 10⁻⁶ C, commonly used in practical applications
  • Nanocoulomb (nC): 10⁻⁹ C, used for small charge measurements

Charge Conservation

  • Conservation Law: Total charge in an isolated system is constant
  • Charge Transfer: Charge can move between objects but cannot be created or destroyed
  • Quantization: Charge comes in discrete units of the elementary charge
  • Neutral Objects: Contain equal amounts of positive and negative charge

🚀 Real-World Applications

⚡ Electronics

Understanding charge interactions in circuits, capacitors, and semiconductor devices.

🧲 Electromagnetism

Foundation for understanding electric fields, magnetic fields, and electromagnetic waves.

🔬 Atomic Physics

Explains electron-proton interactions, atomic structure, and chemical bonding.

⚡ Electrostatics

Understanding static electricity, lightning, and electrostatic phenomena.

🔋 Batteries

Charge separation and storage in batteries and capacitors.

🌩️ Lightning

Charge separation in clouds and discharge through lightning strikes.

🛠️ Calculator Features

Force Analysis

  • Charge Input: Enter charges in coulombs with automatic unit conversion
  • Distance Input: Set separation distance in meters
  • Force Calculation: Automatic calculation of electrostatic force
  • Direction Display: Shows whether force is attractive or repulsive

Advanced Analysis

  • Electric Field: Calculate electric field strength at a point
  • Potential Energy: Determine electrostatic potential energy
  • Visual Charts: Force vs distance and force vs charge relationships
  • Common Examples: Pre-set charge configurations for quick analysis

💡 Examples and Demonstrations

Two 1μC Charges, 10cm Apart

Force = (8.99×10⁹ × 1×10⁻⁶ × 1×10⁻⁶) / (0.1)² = 0.899 N (repulsive)

Electron and Proton in Hydrogen Atom

Force = (8.99×10⁹ × 1.602×10⁻¹⁹ × 1.602×10⁻¹⁹) / (5.29×10⁻¹¹)² = 8.23×10⁻⁸ N (attractive)

Two 1mC Charges, 1m Apart

Force = (8.99×10⁹ × 1×10⁻³ × 1×10⁻³) / (1)² = 8,990 N (repulsive)

💡 Tips for Understanding

Visualize the Forces

  • Draw force vectors for each charge
  • Remember like charges repel, unlike attract
  • Consider the inverse square relationship
  • Use superposition for multiple charges

Practical Applications

  • Observe static electricity effects
  • Notice charge interactions in daily life
  • Think about electronic devices
  • Consider atomic and molecular interactions

Frequently Asked Questions

What is Coulomb's Law?
Coulomb's Law describes the electrostatic force between two charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically: F = k|q₁q₂|/r², where k = 8.99×10⁹ N⋅m²/C² is Coulomb's constant.
How do I use this calculator?
Enter the charges of both particles in coulombs (use scientific notation for small values like 1e-6 for 1 microcoulomb), set the distance between them in meters, and choose your analysis type. The calculator will automatically show the electrostatic force, electric field, and potential energy. You can also click on common examples for typical charge configurations.
What units should I use?
Use SI units: charges in coulombs (C) and distance in meters (m). The calculator automatically converts and displays common prefixes (μC, nC, pC). For example, 1e-6 C = 1 μC (microcoulomb), 1e-9 C = 1 nC (nanocoulomb).
What's the difference between attractive and repulsive forces?
Attractive forces occur between opposite charges (positive and negative) - they pull the charges together. Repulsive forces occur between like charges (both positive or both negative) - they push the charges apart. The calculator shows the direction automatically based on the signs of your charges.
Why does the force decrease with distance squared?
This is called the inverse square law. As distance increases, the force decreases rapidly. If you double the distance, the force becomes 1/4 as strong. If you triple the distance, the force becomes 1/9 as strong. This is because the electric field spreads out in three-dimensional space.
What is Coulomb's constant (k)?
Coulomb's constant k = 8.99×10⁹ N⋅m²/C² is a proportionality constant that makes the equation work with SI units. It's related to the permittivity of free space and ensures that the force calculation gives the correct numerical value in newtons.
How does this relate to electric fields?
The electric field at a point is the force per unit charge that would be experienced by a test charge placed at that point. For a point charge q, the electric field is E = k|q|/r². The calculator shows both the force between two charges and the electric field created by one charge.
What is electrostatic potential energy?
Electrostatic potential energy is the energy stored in the system due to the relative positions of the charges. For two charges, U = kq₁q₂/r. Unlike force, potential energy can be positive or negative depending on whether the charges attract or repel.
Can I use this for multiple charges?
This calculator is designed for two charges. For multiple charges, you would need to use the superposition principle - calculate the force from each charge separately and add them vectorially. The calculator shows the total force between the two specified charges.
What are some real-world examples?
Common examples include: electron-proton attraction in atoms, static electricity between rubbed objects, charge interactions in capacitors, lightning (charge separation in clouds), and electrostatic forces in particle accelerators.
How accurate are the calculations?
The calculations are mathematically accurate based on Coulomb's Law. However, real-world applications may have additional factors like: charge distribution (not point charges), dielectric materials, relativistic effects at high speeds, or quantum effects at very small scales.
What if I get very large or small results?
Check your input values and units. Very large forces might indicate charges that are too large or distances that are too small. Very small forces might indicate charges that are too small or distances that are too large. The calculator uses scientific notation to display very large or small numbers.
How do I interpret the charts?
The Force vs Distance chart shows how force decreases with increasing distance (inverse square relationship). The Force vs Charge chart shows how force changes with the second charge while keeping the first charge and distance constant. The Electric Field chart shows field strength vs distance for a single charge.
What's the difference between this and Newton's law of gravitation?
Both follow inverse square laws, but Coulomb's Law deals with electric charges while Newton's law deals with mass. Electric forces can be attractive or repulsive, while gravitational forces are always attractive. Electric forces are much stronger than gravitational forces for typical charges and masses.
Can this law be violated?
Coulomb's Law is a fundamental law of physics that has been extensively tested and has never been observed to be violated. It applies to all electrostatic interactions. Any apparent violation usually indicates that we haven't accounted for all the charges or forces in the system.

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