Skip to content
Stan’s Legacy
Sign in

Coulomb force between two charges

How hard do two charges at this separation push, or pull, on each other?

The formula
F=ke⁢q1⁢q2r2
F
Force, N
q1
First charge, C
q2
Second charge, C
r
Separation, m
LaTeX 
F = k_e \frac{q1 \cdot q2}{r^2}

Work it out

nC

The charge on the first particle. Negative for a negative charge.

nC

The charge on the second particle.

mm

The distance between them, centre to centre.

or see a worked example with typical numbers

Method

  1. Convert both charges to coulombs and the separation to metres.
  2. Multiply the two charges together — same sign gives a positive product, opposite signs give a negative one.
  3. Divide by the square of the separation: the force falls off very fast with distance, a quarter as much again for every doubling.
  4. Multiply by Coulomb's constant, k_e = 8.9876×10⁹ N·m²/C². A positive result is a repulsive force pushing the charges apart; a negative result is attraction pulling them together.

Assumptions

  • Both charges are treated as points, or as spheres small compared to the separation. Real particles with a finite size and a non-uniform charge distribution depart from this once they are close together.
  • The medium between them is vacuum or air. A conductive or highly polar medium — water, for instance — screens the field and reduces the real force well below this figure.
  • No other charges are present. In a real ionised gas stream a particle feels every other charge nearby, not just the one it is being compared against here.