Coulomb’s Law
F = k · q1 · q2 / r²
Quick answer
This calculator solves F = kₑ × q1 × q2 / r² (kₑ = 8.988×10⁹ N·m²/C²) for Force. With Charge 1 10 µC, Charge 2 22 µC, Separation 10 cm, the result is 0.1977 kN. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Coulomb’s law gives the electrostatic force between two point charges. The force is proportional to the product of the charges and falls off with the square of the distance between them, exactly analogous to gravity. Like charges repel and unlike charges attract. It is the foundation of electrostatics and underlies capacitance, dielectric behaviour, and the forces in every electronic material.
Variables
- F — Electrostatic force (N)
- q1, q2 — The two point charges (C)
- r — Separation between charges (m)
- kₑ — Coulomb constant 8.988×10⁹ N·m²/C²
Practical Notes
The Coulomb constant kₑ = 1/(4πε₀). The inverse-square dependence means halving the distance quadruples the force. In a dielectric medium the force is reduced by the relative permittivity εr.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| F | Force | N | µN, mN, N, kN |
| q1 | Charge 1 | µC | pC, nC, µC, mC, C |
| q2 | Charge 2 | µC | pC, nC, µC, mC, C |
| r | Separation | cm | mm, cm, m, km |
Step by step
- 1. What you know: Charge 1 10 µC, Charge 2 22 µC, Separation 10 cm
- 2. The relation: F = kₑ × q1 × q2 / r² (kₑ = 8.988×10⁹ N·m²/C²)
- 3. Substitute: q1 = 10 µC, q2 = 22 µC, r = 10 cm
- 4. Result: Force = 0.1977 kN
Worked examples
Minimum range
Given: Charge 1 100 nC, Charge 2 0.22 µC, Separation 1 mm
Result: Force = 0.1977 kN
Low range
Given: Charge 1 1 µC, Charge 2 2.2 µC, Separation 10 mm
Result: Force = 0.1977 kN
Typical
Given: Charge 1 10 µC, Charge 2 22 µC, Separation 10 cm
Result: Force = 0.1977 kN
High range
Given: Charge 1 100 µC, Charge 2 0.22 mC, Separation 1 m
Result: Force = 0.1977 kN
Maximum range
Given: Charge 1 1 mC, Charge 2 2.2 mC, Separation 10 m
Result: Force = 0.1977 kN
Solving for each variable
Solve for Force
Charge 1 100 nC, Charge 2 0.22 µC, Separation 1 mm → 0.1977 kN
Solve for Charge 1
Force 1 mN, Charge 2 0.22 µC, Separation 1 mm → 0.5058 pC
Solve for Charge 2
Force 1 mN, Charge 1 100 nC, Separation 1 mm → 1.113 pC
Solve for Separation
Force 1 mN, Charge 1 100 nC, Charge 2 0.22 µC → 44.47 cm
How Force changes with Charge 1
| Charge 1 (input) | Force (result) |
|---|---|
| 1 µC | 19.77 N |
| 2.5 µC | 49.43 N |
| 5 µC | 98.86 N |
| 7.5 µC | 148.3 N |
| 10 µC | 0.1977 kN |
| 15 µC | 0.2966 kN |
| 20 µC | 0.3955 kN |
| 40 µC | 0.7909 kN |
| 70 µC | 1.384 kN |
| 100 µC | 1.977 kN |
The same result in other units
| Unit | Value |
|---|---|
| mN | 197700 |
| N | 197.7 |
| kN | 0.1977 |
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<p><a href="https://vbatpower.com/formulas/coulombs-law/">Coulomb’s Law</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Coulomb’s Law?
Use F = kₑ × q1 × q2 / r² (kₑ = 8.988×10⁹ N·m²/C²). With Charge 1 10 µC, Charge 2 22 µC, Separation 10 cm, Force works out to 0.1977 kN.
What is the formula for Coulomb’s Law?
The formula is F = kₑ × q1 × q2 / r² (kₑ = 8.988×10⁹ N·m²/C²). Coulomb’s law gives the electrostatic force between two point charges.
How do you find Charge 1 when you know the other values?
Rearrange for Charge 1: with Force 1 mN, Charge 2 0.22 µC, Separation 1 mm, Charge 1 is 0.5058 pC.
How do you find Charge 2 when you know the other values?
Rearrange for Charge 2: with Force 1 mN, Charge 1 100 nC, Separation 1 mm, Charge 2 is 1.113 pC.
What units does Coulomb’s Law use?
Force is shown in mN, N, kN. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Fields & Electromagnetism formulas →Need more features?
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