Force Between Two Point Charges Calculator

Calculator

Choose what to solve. Enter signed charges for direction. Use a positive distance and positive force magnitude.

Formula Used

The calculator uses Coulomb law for two point charges:

F = k|q₁q₂| / r²

Here, F is force in newtons. q₁ and q₂ are charges in coulombs. r is separation in meters. k = 1 / (4πε₀εᵣ). In vacuum, k is about 8.9875517923 × 10⁹ N·m²/C².

How to Use This Calculator

1. Select the value you want to calculate.
2. Enter charge one and charge two with correct signs.
3. Enter the separation distance between charge centers.
4. Select the medium or enter a custom relative permittivity.
5. Choose output units and precision.
6. Enter an angle when you need vector components.
7. Press calculate and read the result above the form.
8. Use CSV or PDF buttons to save the result.

Example Data Table

Understanding Coulomb Force

Point charges are ideal charges with no size. They help model small charged objects. Coulomb law predicts the force between them. The force grows when charges get larger. It falls fast when distance increases. Doubling the distance makes the force four times smaller.

Charge Signs Matter

Charge signs control the direction. Two positive charges repel. Two negative charges also repel. Opposite signs attract. The calculator keeps this rule clear. It reports magnitude and interaction type. It also estimates vector components when you enter an angle.

Why Medium Correction Is Useful

Real materials reduce electric force. This happens because electric fields polarize nearby matter. The relative permittivity describes that reduction. Vacuum has a value of one. Air is almost the same. Water is much larger. A larger value means a weaker force. This tool lets you choose common media. You can also enter a custom value.

Working With Units

Physics problems often mix units. A charge may be given in microcoulombs. A distance may be given in centimeters. The calculator converts them internally. It performs the law in standard units. Then it reports clean values in your selected output units. This reduces mistakes during homework and lab reports.

Unknown Values

Advanced use may require solving for a missing value. You can solve for force, either charge, or distance. The same Coulomb equation is rearranged. For unknown charge, the answer is a required magnitude. Its sign depends on the desired interaction. For unknown distance, the answer is the separation that gives the selected force.

Vector Interpretation

A force is not only a size. It also has a direction. When charge one is treated as the reference point, the angle describes where charge two sits. Repulsion points away from the first charge. Attraction points toward it. The x and y components follow that direction. These components help with two dimensional electrostatics.

Uncertainty Notes

Measurements are never perfect. Small errors in charge or distance can affect the result. Distance is especially important. It is squared in the denominator. A one percent distance error can cause about two percent force error. The optional uncertainty fields give a quick estimate.

Practical Tips

Use absolute distances greater than zero. Use signed charges when direction matters. Check the medium before trusting the answer. Vacuum and air are best for many classroom examples. Liquids and solids need correction. Compare the result with the example table. It helps confirm that the entered scale is reasonable.

Result Reading

Very large or tiny answers can look unusual. Scientific notation keeps them readable. One newton is a strong electric force for small lab charges. Millinewtons and micronewtons are common in examples. The sign of each charge is more important than the sign of the final magnitude. Read the attraction or repulsion line before using the components in another equation. This careful habit prevents direction errors in complex force balance work.

FAQs