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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.

Compare with a variation

Result

F Force 0.00036 N

Positive is repulsion (like charges), negative is attraction (opposite charges).

With your numbers
0.00036 N=ke⁢1 nC⁢1 nC5 mm2
LaTeX 
0.00036\,\mathrm{N} = k_e \frac{1\,\mathrm{nC} \cdot 1\,\mathrm{nC}}{5\,\mathrm{mm}^2}

This result is a link — the address bar holds your numbers, so it can be pasted into a post and opened to the same answer.

What this looks like

Force against separation Separation swept from 2.5 mm to 7.5 mm with everything else held at your numbers. The dashed lines cross where you are.
Force against separationForce falls from 0.00144 N to 0.00016 N as separation rises from 2.5 mm to 7.5 mm. At your separation of 5 mm it is 0.00036 N.00.00050.0010.001524685 mm0.00036 NSeparation (mm)Force (N)
The formula behind the curve
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}
What moves the answer Each input moved 10% either way, with the others held still, and the effect on force.
What moves the answerForce is most sensitive to Separation, which moves it by about 23.5% for a 10% change. It is least sensitive to First charge, at about 10%.Change in the answer when each input moves by 10%-40%-20%20%40%Separation±23.5Second charge±10First charge±10
The formula behind the curve
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}

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.