Coulomb's Law Calculator

Online calculator for electrostatic force between charged particles

Calculation

Result
Electrostatic force:


Good to know

What is Coulomb's law?

Coulomb's law describes the electrostatic force between two electrically charged particles. This force is proportional to the product of the charges and inversely proportional to the square of their distance.

Important units
  • Charge (q): C, mC, µC, nC, pC
  • Distance (r): m, cm, mm, µm, nm
  • Force (F): N (Newton)
Example calculation

Two charges: \(q_1 = 20 \text{ nC}\), \(q_2 = 4 \text{ nC}\), distance: \(r = 2 \text{ µm}\)

\[\displaystyle F = k_e \cdot \frac{q_1 \cdot q_2}{r^2}\] \[\displaystyle F = 8{,}988 \times 10^9 \cdot \frac{20 \times 10^{-9} \times 4 \times 10^{-9}}{(2 \times 10^{-6})^2}\]
Coulomb's formula
\[\displaystyle F = k_e \cdot \frac{q_1 \cdot q_2}{r^2}\]
\(k_e = 8{,}988 \times 10^9 \text{ Nm}^2\text{C}^{-2}\) (Coulomb constant)
\(F\) = electrostatic force in Newton
\(q_1, q_2\) = charges in Coulomb
\(r\) = distance in meter

Description of Coulomb's law

Coulomb's inverse square law, or simply Coulomb's law, is an experimental physical law that calculates the force between two electrically charged particles at rest. This electric force is usually called electrostatic force or Coulomb force.

The law states that the magnitude or absolute value of the attractive or repulsive electrostatic force between two point charges is directly proportional to the product of the magnitudes of their charges and inversely proportional to the square of the distance between them. Coulomb discovered that bodies with the same electric charge repel each other.

It follows that the repulsive force that two equally electrified spheres exert on each other is inversely proportional to the square of the distance.

Coulomb also showed that oppositely charged bodies attract each other according to an inverse square law.

Formulas for electrostatic force

Coulomb's law is defined by the following formula:

\[\displaystyle F = k_e \cdot \frac{q_1 \cdot q_2}{r^2}\]
Variables:
  • \(F\) = electrostatic force in Newton
  • \(q_1\) = charge of the 1st object in Coulomb
  • \(q_2\) = charge of the 2nd object in Coulomb
  • \(r\) = distance between the objects in meter
Coulomb constant:
\[k_e = 8{,}987{,}551{,}787{,}368 \times 10^9 \text{ Nm}^2\text{C}^{-2}\]

Approximation: \(k_e \approx 8{,}988 \times 10^9 \text{ Nm}^2\text{C}^{-2}\)

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