Coulomb’s Law Calculator
Determine the electrostatic force between two point charges based on Coulomb’s Law.
This shows the magnitude of the electrostatic force. A positive result indicates repulsion, while a negative result indicates attraction.
Intermediate Values
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Force vs. Distance Chart
What is Coulomb’s Law?
Coulomb’s Law is a fundamental principle in physics that describes the electrostatic interaction between electrically charged particles. Published by French physicist Charles-Augustin de Coulomb in 1785, the law quantifies the force exerted by one charged particle on another. It states that this force is directly proportional to the product of the magnitudes of the two charges and inversely proportional to the square of the distance between their centers. Coulomb’s law can be used to calculate the electrostatic force, which can be either attractive or repulsive.
This law is essential for anyone studying or working in fields related to electromagnetism, from electrical engineering students to physicists. It helps explain everything from the stability of atoms to the design of electronic components. A common misunderstanding is confusing electrostatic force with gravity; while both are inverse-square laws, the Coulomb force is vastly stronger and can be either attractive (opposite charges) or repulsive (like charges), whereas gravity is always attractive.
The Coulomb’s Law Formula and Explanation
The mathematical expression for Coulomb’s Law is straightforward yet powerful. It allows for precise calculation of the electrostatic force (F) between two point charges.
F = k * |q₁ * q₂| / r²
This formula is the core of our Coulomb’s Law Calculator. The result indicates the magnitude of the force. The nature of the force (attraction or repulsion) is determined by the signs of the charges (q₁ and q₂). If you are looking for more details on related electrical principles, you might be interested in our Ohm’s Law Calculator.
| Variable | Meaning | Standard Unit (SI) | Typical Range |
|---|---|---|---|
| F | Electrostatic Force | Newtons (N) | Piconewtons to Meganewtons |
| k | Coulomb’s Constant | N·m²/C² | ~8.988 × 10⁹ (in vacuum) |
| q₁, q₂ | Point Charges | Coulombs (C) | nC to kC |
| r | Distance between centers | Meters (m) | Micrometers to kilometers |
Practical Examples
Understanding the application of the Coulomb’s Law Calculator is best done through examples.
Example 1: Repulsive Force
Imagine two small conductive spheres, one with a positive charge and one also with a positive charge, held in a lab.
- Input q₁: +2.0 µC (microcoulombs)
- Input q₂: +5.0 µC (microcoulombs)
- Input r: 10 cm
Using the calculator, we convert 10 cm to 0.1 m. The force calculation would be:
F = (8.988 × 10⁹) * |(2.0 × 10⁻⁶ C) * (5.0 × 10⁻⁶ C)| / (0.1 m)² ≈ 8.988 N.
Since both charges are positive, the resulting force is repulsive.
Example 2: Attractive Force
Now consider a proton and an electron in a hydrogen atom, a classic electrostatics problem.
- Input q₁ (proton): +1.602 × 10⁻¹⁹ C
- Input q₂ (electron): -1.602 × 10⁻¹⁹ C
- Input r (avg. radius): 53 picometers (5.3 x 10⁻¹¹ m)
The force is: F = (8.988 × 10⁹) * |(1.602e-19) * (-1.602e-19)| / (5.3e-11)² ≈ -8.2 × 10⁻⁸ N.
The negative sign indicates an attractive force, which keeps the electron in orbit. To learn more about charge, see our article What is Electric Charge?.
How to Use This Coulomb’s Law Calculator
- Enter Charge 1 (q₁): Input the value of the first charge. Use the dropdown to select the appropriate unit (Coulombs, microcoulombs, or nanocoulombs).
- Enter Charge 2 (q₂): Input the value of the second charge and select its unit. Remember that opposite signs result in attraction.
- Enter Distance (r): Provide the distance between the centers of the two charges and select the unit (meters, cm, or mm).
- Interpret the Results: The calculator instantly provides the electrostatic force in Newtons. The sign of the result tells you if the force is attractive (-) or repulsive (+). Intermediate values show your inputs converted to standard SI units.
Key Factors That Affect Electrostatic Force
Several factors directly influence the outcome of the Coulomb’s Law calculation. Understanding them provides deeper insight into electrostatics.
- Magnitude of Charges: The force is directly proportional to the product of the charges. Doubling one charge doubles the force.
- Distance: As an inverse-square law, distance has a powerful effect. Doubling the distance reduces the force to one-quarter of its original value.
- Sign of Charges: Like charges (both positive or both negative) repel each other. Opposite charges (one positive, one negative) attract.
- The Medium (Dielectric Constant): The calculations here assume a vacuum (or air). Placing charges in a different medium, like water, reduces the force because the medium’s molecules shield the charges from each other.
- Point Charge Assumption: The law is most accurate for point charges or spheres where charge is uniformly distributed. For irregularly shaped objects, the calculation is more complex.
- System of Charges: If more than two charges are present, the net force on one charge is the vector sum of the forces from all other charges. This principle is called superposition. For more on this, read about Electric Field Superposition.
Frequently Asked Questions (FAQ)
By convention in many physics contexts, a positive force value indicates repulsion (the charges are pushed apart), while a negative force value indicates attraction (the charges are pulled together).
It’s called an inverse-square law because the force is inversely proportional to the square of the distance (r²). If you triple the distance, the force decreases by a factor of nine (3²).
Coulomb’s Constant (k) is a proportionality constant that relates the units of charge and distance to the unit of force. Its value in a vacuum is approximately 8.988 × 10⁹ N·m²/C².
No, this tool calculates the force between exactly two point charges. To find the net force in a system with multiple charges, you would use this calculator for each pair and then perform a vector sum of the results, a concept known as superposition.
The formula involves division by r², so a distance of zero would lead to a mathematical singularity (division by zero), implying an infinite force. In reality, point charges cannot occupy the exact same space. The calculator will show an error if you enter zero for the distance.
Both Coulomb’s Law and Newton’s Law of Universal Gravitation are inverse-square laws describing a force between two bodies. However, gravitational force is always attractive and is many orders of magnitude weaker than the electrostatic force.
You can input charges in Coulombs (C), microcoulombs (µC), or nanocoulombs (nC), and distance in meters (m), centimeters (cm), or millimeters (mm). All inputs are converted to standard SI units (C and m) for the calculation, and the result is given in Newtons (N).
It’s fundamental to technology. It governs how transistors work, how xerography (photocopying) functions, and is crucial in designing particle accelerators, air purifiers, and understanding molecular bonds in chemistry. If you are interested in other fundamental forces, check out our Gravitation Calculator.