Calculator
Formula Used
Pair force magnitude:
F = k |qa qb| / r2
Vector force on target charge i by source charge j:
Fij,x = k qi qj (xi - xj) / r3
Fij,y = k qi qj (yi - yj) / r3
Net force:
Fx = ΣFij,x, Fy = ΣFij,y
Fnet = √(Fx2 + Fy2)
θ = atan2(Fy, Fx)
Medium adjustment:
keffective = 8.9875517923 × 109 / εr
How to Use This Calculator
- Enter the three charge values.
- Select the correct unit for each charge.
- Enter x and y positions for each charge.
- Choose one coordinate unit for all positions.
- Select the target charge for net force calculation.
- Enter relative permittivity for the medium.
- Press Calculate to view force, field, and energy results.
- Use CSV or PDF export for saving the answer.
Example Data Table
| Charge | Value | Unit | X Position | Y Position | Coordinate Unit |
|---|---|---|---|---|---|
| q1 | 2 | uC | 0 | 0 | m |
| q2 | -3 | uC | 0.30 | 0 | m |
| q3 | 1.5 | uC | 0 | 0.40 | m |
About Three Charge Coulomb Calculations
Why Three Charges Need Vectors
Coulomb's law explains how electric charges push or pull each other. A three charge problem is more detailed than a two charge problem. One charge can feel force from two separate sources. Each pair force has its own size and direction.
How This Tool Works
This calculator treats every charge as a point charge. It also uses two dimensional coordinates. The target charge is selected by the user. The tool then finds the force from each other charge on that target. Finally, it adds the x and y components to give one net force.
Direction and Sign
Direction matters in this calculation. A positive product of charges means repulsion. A negative product means attraction. The coordinate positions decide the actual direction of each vector. That is why component form is helpful. It prevents sign mistakes and makes angled layouts easier to solve.
Medium Effect
The relative permittivity field lets you model different media. Air and vacuum are close to one. Water, oil, glass, and other materials can reduce the force. The calculator divides Coulomb's constant by this value. Use a trusted value when accuracy is important.
Result Meaning
Results include pair force, net force, angle, electric field, and potential energy. The electric field is useful when you want the field at the target point. Potential energy helps compare charge arrangements. These values can support homework, lab notes, design checks, and quick teaching examples.
Good Input Practice
Use consistent coordinates for the best result. Select one coordinate unit for all positions. Enter charges with their matching unit. Do not place two charges at the exact same point. That creates zero distance, and the formula becomes undefined.
Important Limits
This tool is meant for ideal electrostatic cases. It does not include charge size, surface shape, motion, magnetic effects, or shielding by conductors. It also assumes charges are fixed while the force is calculated. For real systems, compare the result with engineering standards or lab measurements.
Saving Results
The export buttons make the calculator practical for records. Download the CSV for spreadsheets. Download the PDF for a quick report. Always keep the input values with the answer. Small unit changes can produce very large force changes in electrostatic problems.
Rounding is shown clearly. Scientific notation keeps tiny charges readable and large forces easier to compare across examples during study sessions too.
FAQs
What does this calculator find?
It finds the net electric force on one selected charge. It uses the other two charges as force sources. It also shows force components, angle, electric field, potential, and energy values.
Can I choose which charge receives the force?
Yes. Use the target charge field. The calculator then computes the force on that selected charge due to the remaining two charges.
Why are x and y positions needed?
Positions define the distance and direction between charges. Without coordinates, the calculator can find only simple line forces, not complete two dimensional vector results.
What is relative permittivity?
Relative permittivity describes how a medium affects electric force. Vacuum and air are near one. Higher values reduce the effective Coulomb force between charges.
Can I enter negative charges?
Yes. Negative signs are important. They decide whether each pair interaction is attractive or repulsive. The calculator keeps the sign in vector calculations.
What happens if two charges share one point?
The calculator shows an error. Coulomb's law uses distance in the denominator. A zero distance makes the result undefined and physically unrealistic for point charges.
Are the results exact for real objects?
No. The calculator assumes ideal point charges. Real objects may have size, shape, motion, shielding, or charge distribution effects that change the result.
Why use scientific notation?
Electrostatic values can become very small or very large. Scientific notation keeps results readable, especially when using microcoulombs, nanocoulombs, or short distances.