Example Data Table
| Charge |
Value |
Unit |
x |
y |
z |
Coordinate Unit |
| q1 |
5 |
µC |
0 |
0 |
0 |
m |
| q2 |
-3 |
µC |
0.4 |
0 |
0 |
m |
| q3 |
2 |
µC |
0 |
0.3 |
0 |
m |
Formula Used
The calculator uses Coulomb law in vector form.
Fij = k qi qj (ri − rj) / |ri − rj|³
k = 8.9875517923 × 10⁹ / εr
Net force on charge i = Σ Fij
Potential energy for each pair = k qi qj / rij
Here, qi and qj are charges in coulombs. Position vectors are in meters. εr is the relative permittivity of the medium.
How to Use This Calculator
- Enter each charge value with its unit.
- Enter x, y, and z coordinates for all three charges.
- Select the coordinate unit used by all positions.
- Enter the relative permittivity of the medium.
- Choose the decimal precision for displayed answers.
- Press the calculate button.
- Review net force, pair force, angles, and energy.
- Use the CSV or PDF button to save results.
Understanding Three Charge Force
Electric force between three point charges is a vector problem. Each charge feels a force from the other two charges. The calculator applies Coulomb law to every pair. It then adds the vector parts for each charge. This gives a net force in newtons. The sign of each charge matters. Like charges repel. Opposite charges attract. Position also matters. A small change in distance can change the answer strongly.
Why Vector Addition Matters
For three charges, force is not found with one simple distance. Each interaction has its own direction. The force on charge one from charge two may point left. The force from charge three may point upward. The final result is the vector sum. This is why x, y, and z coordinates are useful. They allow the calculator to work with angled or three dimensional layouts. Magnitude alone can hide the direction. Components show how the force acts in space.
Using Units Correctly
Charge can be entered in coulombs, millicoulombs, microcoulombs, or nanocoulombs. Coordinates can use meters, centimeters, millimeters, or kilometers. The calculator converts these values before calculation. This keeps the formula consistent. The relative dielectric value adjusts the electric constant. Use one for vacuum or air in basic homework. Use a larger value when the charges are in an insulating medium.
Interpreting the Results
The pair force table shows each separate interaction. The net force table shows the final effect on every charge. Angles are measured from the positive axes. Elevation shows how much the vector rises above the xy plane. Potential energy is also listed for each pair. It helps compare stable and unstable arrangements. The system check should be near zero. This follows Newton third law. Small nonzero values can appear because computers round decimal numbers.
Physics Study Benefits
This tool supports lab reports, class examples, and quick design checks. It also helps students see why vectors are important. Try moving one charge while keeping the others fixed. Watch the components and angles change. That simple test builds a strong understanding of electric interaction.
Good habits improve accuracy. Enter signed charges carefully. Use matching geometry units. Avoid zero distance. Compare the exported file with your notes before sharing final numeric answers.
FAQs
What does this calculator find?
It finds the pairwise electric forces and the net force acting on each of three point charges. It also shows vector components, direction angles, electric field magnitude, and potential energy.
Can I enter negative charges?
Yes. Negative signs are important. Positive and negative charges attract each other. Charges with the same sign repel each other. The calculator uses the sign when building force vectors.
Why are coordinates needed?
Coordinates define distance and direction between charges. Three point charges may not lie on one line. Vector coordinates let the calculator handle two dimensional and three dimensional arrangements.
What value should I use for relative permittivity?
Use 1 for vacuum or basic air examples. Use a higher value when a dielectric medium is present. The calculator divides Coulomb constant by this value.
Why is the system force check near zero?
Internal electric forces occur in equal and opposite pairs. When all net forces are added, the total should be near zero. Tiny values may appear from rounding.
What is alpha, beta, and gamma?
Alpha is the angle from the positive x axis. Beta is from the positive y axis. Gamma is from the positive z axis. These angles describe vector direction.
Can this calculator handle charges at the same point?
No. Coulomb law becomes undefined at zero distance. The calculator stops and asks for different positions when two charges share the same coordinates.
What is the CSV export used for?
The CSV file saves calculated values in table format. It is useful for homework records, lab reports, spreadsheets, and checking repeated examples.