Coulomb's Law Calculator
Calculate electrostatic force and electric field between point charges using Coulomb's Law
How to Use
- Enter the magnitude of the first charge
- Enter the magnitude of the second charge
- Enter the distance between the charges
- Select the medium (vacuum, air, water, etc.)
- Choose your preferred units
- Click calculate to see force and field strength
What is Coulomb's Law?
Coulomb's Law describes the electrostatic force between two point charges. It states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
This fundamental law of electrostatics was discovered by Charles-Augustin de Coulomb in 1785 and forms the basis for understanding electrical interactions at the atomic and molecular level.
Coulomb's Law Formula
The mathematical expression of Coulomb's Law is:
F = k × |q₁ × q₂| / (εᵣ × r²)
Where:
- F = electrostatic force (N)
- k = Coulomb's constant (8.99 × 10⁹ N⋅m²/C²)
- q₁, q₂ = magnitudes of the two charges (C)
- εᵣ = relative permittivity of the medium
- r = distance between charges (m)
Force Direction
The direction of the electrostatic force depends on the signs of the charges:
- Like charges (both positive or both negative): Repulsive force
- Unlike charges (one positive, one negative): Attractive force
The force acts along the line connecting the two charges and follows Newton's third law (equal and opposite forces).
Electric Field
The electric field at a point due to a charge is:
E = k × |q| / (εᵣ × r²)
The electric field represents the force per unit charge that would be experienced by a test charge placed at that point.
Applications of Coulomb's Law
- Atomic physics: Understanding electron-proton interactions
- Molecular chemistry: Explaining chemical bonding
- Electrostatic precipitators: Air pollution control
- Inkjet printers: Precise droplet positioning
- Electrostatic painting: Uniform coating application
- Capacitor design: Energy storage devices
- Particle accelerators: Charged particle manipulation
Frequently Asked Questions
- What is the difference between Coulomb's Law and Newton's Law of Gravitation?
- Both laws have similar mathematical forms (inverse square law), but Coulomb's Law deals with electric charges and can be either attractive or repulsive, while Newton's Law of Gravitation deals with masses and is always attractive. Also, electrostatic forces are much stronger than gravitational forces.
- Why does the medium affect the electrostatic force?
- The medium affects the force through its relative permittivity (εᵣ). In a medium with higher permittivity, the electric field is reduced, resulting in a weaker force. This is because the medium's molecules become polarized, partially canceling the electric field.
- Can Coulomb's Law be used for non-point charges?
- Coulomb's Law in its basic form applies only to point charges. For extended charge distributions, you need to use integration or other methods like Gauss's Law. However, for charges separated by much larger distances than their sizes, point charge approximation works well.
- What happens when the distance between charges approaches zero?
- As distance approaches zero, the force approaches infinity according to Coulomb's Law. In reality, this doesn't happen because charges have finite size and quantum mechanical effects become important at very small distances.
- How accurate is Coulomb's Law in real applications?
- Coulomb's Law is extremely accurate for macroscopic charges at reasonable distances. It breaks down at very small distances (quantum scale) or very high speeds (relativistic effects), but for most practical applications in engineering and physics, it provides excellent results.