Find charge separation from Coulomb force
Use signed charges. Enter force as a positive magnitude.
Formula used
F = (k0 / εr) × |q1q2| / r²
r = √[k0 × |q1q2| / (εr × F)]
F is force magnitude, r is separation distance, and εr is relative permittivity.
The vacuum constant k0 equals 8.9875517923 × 109 N·m²/C².
How to use this calculator
- Enter the first and second charge values. Keep their signs.
- Choose the matching unit for each charge.
- Enter the observed force magnitude and its unit.
- Set relative permittivity for the surrounding material.
- Choose the distance unit and decimal precision.
- Calculate the range, then export or print the result.
Example data
| Charge A | Charge B | Force | Relative permittivity | Expected range |
|---|---|---|---|---|
| +2 μC | −3 μC | 0.54 N | 1.00 | 0.316 m |
| +50 nC | +80 nC | 0.20 mN | 2.50 | 0.268 m |
Understanding Coulomb Force Range
Electric force links charged objects across empty space or material. Its strength changes with charge size and separation. This calculator reverses the common relationship. It estimates separation distance when two charges and a measured force are known. The result helps check laboratory readings, plan demonstrations, compare electrostatic systems, and understand how force changes across different distances.
Coulomb’s law describes the interaction between two point charges. It uses the product of their charge magnitudes. It divides that product by the square of their separation. Therefore, distance has a strong effect. Doubling distance reduces force to one quarter. Halving distance makes force four times greater. Small measuring errors can produce meaningful range changes.
The calculator accepts positive or negative charge values. The signs identify interaction type. Matching signs repel each other. Opposite signs attract each other. Distance uses the magnitude of force, because a physical separation cannot be negative. The result card states whether the interaction is attractive or repulsive. This helps you interpret the direction separately from range.
Charge units can strongly affect the answer. A coulomb is large for many laboratory examples. Microcoulombs and nanocoulombs are common choices. The calculator converts every selected unit to coulombs before applying the formula. Force units are also converted to newtons. These internal conversions prevent manual exponent mistakes and make values easier to enter.
A dielectric medium changes electrostatic interaction. Air is usually close to vacuum for introductory calculations. Water and some insulating materials reduce effective force more substantially. Enter the relative permittivity when a medium surrounds both charges. The calculator divides the vacuum constant by this value. A larger relative permittivity gives a shorter calculated range for the same observed force.
Use measured values that describe isolated point-like charges. The equation is most reliable when charge sizes are small compared with their separation. It is less accurate for extended objects, uneven charge distributions, moving charges, or nearby conducting surfaces. In those cases, field geometry can alter the force. Treat the answer as an idealized estimate, then compare it with experiment.
Choose a display unit that matches your situation. Millimeters work well for close demonstrations. Centimeters suit tabletop setups. Meters suit larger experimental spacing. The scientific notation result is useful for very small ranges. The included verification line recalculates force from the displayed range. It provides a fast check that the entered units and dielectric setting were applied correctly.
Careful rounding improves communication. Keep several digits while entering measurements. Then select a sensible number of decimal places for reporting. Do not claim precision beyond the instruments you used. Record charge units, force units, medium, and temperature assumptions with your results. Clear notes make another calculation easier to reproduce and make unexpected differences easier to investigate.
Teachers explain why electrostatic models need stated conditions. Written records support repeated classroom checks and laboratory discussions. These practices reveal assumptions behind every reported numerical estimate more clearly today.
Frequently asked questions
1. What does this calculator find?
It finds the separation distance between two charged objects from their charges, observed force magnitude, and relative permittivity.
2. Which equation does it use?
It rearranges Coulomb’s law to solve distance. The charge product is divided by force and relative permittivity, then square rooted.
3. Do charge signs change the calculated range?
The range uses charge magnitudes. Signs identify whether the interaction is attractive or repulsive, not whether the separation is positive.
4. Why is relative permittivity needed?
Relative permittivity accounts for the surrounding medium. It reduces the effective electrostatic constant compared with vacuum.
5. Which charge units can I enter?
You can enter coulombs, millicoulombs, microcoulombs, nanocoulombs, or picocoulombs. The calculator converts them internally.
6. Can I calculate ranges for identical signs?
Yes. Charges with matching signs repel. Their force magnitude still determines a valid positive separation range.
7. Should the force value be negative?
No. Enter a positive force magnitude. The signs of the charges already describe attraction or repulsion.
8. What does the force check show?
It recalculates force from the solved range. It should closely match your converted input force, apart from rounding.
9. Is this suitable for large charged objects?
It is best for point-like charges or objects much smaller than their separation. Large objects need more detailed field models.
10. Why might a laboratory result differ?
Nearby surfaces, charge leakage, uneven distribution, motion, humidity, and measurement uncertainty can all alter observed force.
11. How can I save the result?
After calculation, use Download CSV for a data file. Use Print / Save PDF for a shareable report.