Electrostatic interaction
What is Coulomb's law?
Coulomb's law describes the magnitude of the electric force between two stationary point charges. The force increases with charge magnitude and decreases rapidly as distance increases.
The relationship is an inverse-square law, meaning that doubling the separation distance reduces the force to one quarter of its original value.
Main equation
Coulomb's law formula
Electrostatic forceF = kq₁q₂ ÷ r²
- F is force in newtons.
- q₁ and q₂ are charge magnitudes in coulombs.
- r is centre-to-centre separation distance in metres.
- kis Coulomb's constant.
Rearranged equations
Solve for charge or distance
First charge
q₁ = Fr² ÷ kq₂
Second charge
q₂ = Fr² ÷ kq₁
Distance
r = √(kq₁q₂ ÷ F)
Worked example
Find electrostatic force
- Let q₁ = 1 × 10⁻⁶ C.
- Let q₂ = 2 × 10⁻⁶ C.
- Let separation distance be 0.05 m.
- Apply F = kq₁q₂ ÷ r².
- The force magnitude is approximately 7.19 N.
Attraction and repulsion
Charge signs determine direction
Charges with the same sign repel each other. Charges with opposite signs attract each other.
This calculator uses positive charge magnitudes and reports the magnitude of the force. Determine direction separately from the signs of the charges.
Unit guidance
Convert charge values to coulombs
- 1 microcoulomb = 1 × 10⁻⁶ C.
- 1 nanocoulomb = 1 × 10⁻⁹ C.
- 1 millimetre = 1 × 10⁻³ m.
- Force is reported in newtons.
Model limitations
Assumptions and limitations
Coulomb's law in this form assumes stationary point charges in vacuum or approximately in air. The separation distance must be measured between the charge centres.
Extended charge distributions, dielectric materials, moving charges, shielding, and complex electric-field geometries may require more advanced models.
Related tools
Continue your force analysis
Use the Force Calculator to calculate force, mass, or acceleration using Newton's second law.
Use the Ohm's Law Calculator to analyze voltage, current, resistance, and electrical power.
Questions and answers
Coulomb's law calculator FAQ
What formula does the Coulomb's law calculator use?
The calculator uses F = kq₁q₂ / r², where F is electrostatic force, q₁ and q₂ are charge magnitudes, r is separation distance, and k is Coulomb's constant.
What value is used for Coulomb's constant?
The calculator uses approximately 8.9875517923 × 10⁹ newton metre squared per coulomb squared.
What units should I enter?
Enter force in newtons, charge magnitudes in coulombs, and separation distance in metres.
Can I enter microcoulombs or nanocoulombs?
Yes, after converting them to coulombs. For example, 1 microcoulomb is 1 × 10⁻⁶ coulombs and 1 nanocoulomb is 1 × 10⁻⁹ coulombs.
Does the calculator determine attraction or repulsion?
The calculator determines force magnitude only. Charges with the same sign repel, while charges with opposite signs attract.