Formula used
This calculator uses Coulomb’s law for point charges: F = k · |q1·q2| / r². Here, q1 and q2 are charges in coulombs, r is the separation distance in meters, and F is the force in newtons.
The constant k depends on the medium: k = k₀ / εr, where k₀ ≈ 8.99×10⁹ N·m²/C² and εr is the relative permittivity. Larger εr means stronger screening and a smaller force.
Signs determine the interaction type: like charges repel and unlike charges attract. The reported value is the magnitude; the note explains direction.
How to use this calculator
- Select what you want to solve for: force, distance, or a charge.
- Enter q1 and q2 with signs and units.
- Enter the separation distance r and choose its unit.
- If solving for distance or charge, enter the given force value too.
- Pick the medium (or enter a custom εr), then press Calculate.
- Use the CSV or PDF buttons to export your results.
Example data
| q1 | q2 | r | Medium (εr) | Force magnitude (N) | Interaction |
|---|---|---|---|---|---|
| +2 μC | −3 μC | 0.05 m | Air (1.0) | 21.57 | Attraction |
| +10 nC | +10 nC | 0.10 m | Air (1.0) | 0.0000899 | Repulsion |
| +1 mC | −0.5 mC | 2.0 m | Air (1.0) | 1123.4 | Attraction |
| +5 μC | +5 μC | 0.02 m | Water (80.1) | 7.02 | Repulsion |
| +100 pC | −50 pC | 1 mm | Glass (4.7) | 0.00000956 | Attraction |
| −4 μC | −1 μC | 0.30 m | Air (1.0) | 0.399 | Repulsion |
| +25 nC | −60 nC | 5 cm | Plastic (2.5) | 0.002157 | Attraction |
| +0.2 mC | +0.2 mC | 0.50 m | Mineral oil (2.2) | 653.64 | Repulsion |
| +3 μC | −3 μC | 1 cm | Air (1.0) | 808.88 | Attraction |
| +2 nC | +5 nC | 2 mm | Rubber (7.0) | 0.00321 | Repulsion |
Example forces are rounded for readability.
Electrostatic force guide
Coulomb’s law in practical units
In vacuum or air, k0 ≈ 8.99×10⁹ N·m²/C². If q1 = +1 μC and q2 = +1 μC at r = 0.01 m, the force is about 89.9 N. At 0.10 m, it drops to about 0.899 N, showing how fast spacing changes results.
Why distance dominates
The relationship is inverse‑square: F ∝ 1/r². Doubling distance cuts force by 4; tripling cuts it by 9. For the same 1 μC and 1 μC pair in air: r=2 cm → ~22.5 N, r=5 cm → ~3.60 N, r=20 cm → ~0.225 N.
Choosing realistic charge sizes
Lab electrostatics often uses nC to μC values. A small rubbed plastic rod can carry tens of nC, while charged metal spheres can reach μC levels with proper insulation. Very large values (mC) are uncommon in air because corona and breakdown can leak charge away.
Medium matters through εr
Materials reduce force through relative permittivity εr because k = k0/εr. Air is ≈1.0, mineral oil ≈2.2, plastic ≈2.5, glass ≈4.7, rubber ≈7.0, and water ≈80.1. The same charges and distance in water produce roughly 1/80 of the air‑value.
Sign and direction interpretation
The calculator reports magnitude using |q1·q2|, then labels the interaction. Like signs (+/+ or −/−) repel, unlike signs attract. Direction is along the line connecting centers: each charge experiences equal magnitude, opposite direction, consistent with Newton’s third law.
Solving backward for r or charge
If you know force and charges, compute distance with r = √(k|q1q2|/F). If you know force, distance, and one charge, solve the other with |q| = Fr²/(k|qknown|). This tool keeps your chosen sign while calculating the required magnitude.
Measurement tips and limitations
Use center‑to‑center spacing, not edge spacing. Keep conductors on insulating stands, and avoid touching them after charging. Humidity increases leakage, reducing measured force over time. Coulomb’s law assumes point charges and no nearby grounded objects; real setups can deviate. If forces seem too high, recheck units: μC versus nC and cm versus m. A tenfold unit slip can change the force by one hundredfold.
FAQs
1) What constant does the calculator use for k?
It starts with k0 ≈ 8.9875517923×10⁹ N·m²/C² (vacuum) and adjusts for the selected medium using k = k0/εr. This matches common textbook and lab reference values.
2) Why is the result always a positive number?
The force shown is the magnitude, computed with |q1·q2|. Direction is handled separately: the calculator labels attraction or repulsion based on signs, then gives a short direction note.
3) Why does selecting water reduce the force so much?
Water has a large relative permittivity (about 80), so it strongly screens electric fields. Since k = k0/εr, the same charges and distance produce roughly 1/80 of the force compared with air.
4) Can I use this for plates or extended objects?
This tool assumes point charges separated by a straight‑line distance. Large plates, rings, or irregular shapes can have different field distributions, so Coulomb’s point‑charge formula may not fit. Use it for first‑pass estimates or for small spheres.
5) How do I convert μC or nC to coulombs?
Use metric prefixes: 1 μC = 1×10⁻⁶ C, 1 nC = 1×10⁻⁹ C, and 1 pC = 1×10⁻¹² C. The calculator converts your chosen units to SI internally for consistent results.
6) What happens if I enter a very small distance?
Force grows rapidly as r approaches zero because of the 1/r² term. In real life, charges redistribute, air can break down, and surfaces touch, so the ideal model stops being valid.