Calculator
Example data table
| # | q1 | q2 | r | er | Expected interaction | Force scale |
|---|---|---|---|---|---|---|
| 1 | +2.5 uC | -1.2 uC | 5 cm | 1 | Attractive | ~ 10 N |
| 2 | +40 nC | +40 nC | 10 cm | 2.5 | Repulsive | ~ 0.06 N |
| 3 | -1.0 uC | -1.0 uC | 1 mm | 3 | Repulsive | ~ 3,000 N |
Formula used
Coulomb’s law gives the magnitude of the electrostatic force between two point charges: F = (k/er) * |q1*q2| / r^2.
- F is force magnitude in newtons (N).
- k is Coulomb’s constant.
- er is relative permittivity of the medium.
- q1, q2 are charges in coulombs (C).
- r is separation distance in meters (m).
How to use this calculator
- Enter q1 and q2 with sign and unit.
- Enter the separation distance r and choose its unit.
- Set er for the medium (use 1 for air).
- Optionally set angle theta to get Fx and Fy.
- Pick an output unit and press Calculate Force.
- Use the CSV/PDF buttons to export the latest result.
Article
Charge and distance ranges
Coulomb force becomes practical when you choose realistic magnitudes. Classroom problems often use 10–500 nC or 0.1–10 uC charges, with separations from 1 mm to 50 cm. At 1 uC and 1 cm in air, the force is about 90 N, comparable to holding a 9 kg mass. At 1 uC and 10 cm, it drops near 0.9 N.
Medium effects with relative permittivity
The calculator divides by er to model dielectrics. Air is near 1.0, common plastics sit around 2–4, and distilled water is near 80. If you keep q1, q2, and r fixed, raising er from 1 to 4 reduces force by 75%, which is why insulators weaken interactions.
Inverse square sensitivity
Because F scales with 1/r^2, small distance errors dominate. Halving r multiplies force by 4; doubling r cuts force to 25%. A change from 5 cm to 4 cm increases force by (5/4)^2 ≈ 1.56, a 56% jump. If your ruler uncertainty is 1 mm at r = 10 mm, that is a 10% distance error and roughly a 20% force error. The plotted curve highlights this steep region.
Direction, components, and sign meaning
The magnitude uses |q1 q2|, while attraction or repulsion depends on the sign of q1*q2. When you set an angle, the tool resolves Fx and Fy using cos(theta) and sin(theta). This is useful when the force vector is aligned with an axis in a diagram, or when comparing two perpendicular contributions in a multi-charge setup.
Uncertainty and tolerance band
Measurements of charge and spacing carry uncertainty. The optional tolerance band applies a +/- percent range to the computed magnitude, producing Fmin and Fmax. For a 5% band around 2.00 N, the range becomes 1.90 to 2.10 N, supporting lab reporting. If your charge estimate is +/-3% and distance is +/-2%, a quick combined estimate is about +/-7% on force.
Unit conversion and reporting workflow
Inputs accept C, mC, uC, nC, and pC, then convert to coulombs internally. Distances accept m, cm, mm, um, and nm, converting to meters. Exporting CSV preserves SI values, interaction, angle, and tolerance settings. The PDF summarizes parameters and results, making it easy to attach a page to homework, notes, or a troubleshooting log.
FAQs
1) What does the sign of each charge change?
It changes the interaction type. Like signs repel and opposite signs attract. The calculator uses the sign of q1*q2 to label the interaction while keeping the magnitude positive.
2) Why does the graph use logarithmic axes?
Force and distance can span many orders of magnitude. Log axes keep small and large values readable and make the 1/r^2 trend appear as a straight line.
3) What value should I use for er in air?
Use 1.0 for most homework and quick checks. Dry air is extremely close to 1, so the difference is usually negligible at typical problem precision.
4) Are these results valid for extended objects?
They are most accurate for point charges or objects small compared with r. For large spheres, plates, or distributed charge, field methods or numerical models may be needed.
5) How are Fx and Fy computed?
The tool treats the force magnitude as F and applies Fx = F cos(theta) and Fy = F sin(theta). Theta is measured from the positive x axis.
6) What does the tolerance band represent?
It is a simple +/- percent range applied to the force magnitude to reflect uncertainty. It does not propagate separate errors for q and r, but it is useful for quick lab-style ranges.