Enter Particle and Field Data
All fields use SI units. Zero values disable the matching contribution.
Example Input Data
| Quantity | Particle 1 | Particle 2 |
|---|---|---|
| Mass | 2 kg | 3 kg |
| Charge | +2.0 × 10-6 C | -3.0 × 10-6 C |
| Position | (0, 0, 0) m | (0.50, 0, 0) m |
| Velocity | (4, 0, 0) m/s | (0, 2, 0) m/s |
| Shared fields | E = (150, 0, 0) V/m; B = (0, 0, 0.20) T; g = (0, 0, -9.80665) m/s² | |
Formula Used
r₁₂ = r₂ − r₁, r = |r₁₂|, r̂₁₂ = r₁₂ / rFg,1 = Gm₁m₂r̂₁₂ / r²Fe,1 = −kq₁q₂r̂₁₂ / r²FE = qE, FB = q(v × B), Fweight = mgFdrag = −½ρCdA|v − u|(v − u)Fnet = ΣF, a = Fnet / mHow to Use This Calculator
- Enter a positive mass and charge for each particle.
- Provide different x, y, and z positions in metres.
- Add velocities when magnetic or drag forces matter.
- Enter external electric, magnetic, and gravity field components.
- Supply fluid data only when quadratic drag applies.
- Add manual components for forces outside the built-in models.
- Select Calculate All Forces and read the result above.
- Export the summary when you need a calculation record.
Understanding Two-Particle Forces
Vector Direction Matters
A two-particle force problem becomes clearer when every quantity is expressed as a vector. A scalar magnitude alone cannot describe a push or pull in three dimensions. Position coordinates establish separation. The separation vector identifies the line joining both particles. Its unit vector supplies direction. The calculator then adds each selected force component before finding a net result.
Mutual Forces
Mutual gravity always attracts positive masses. Its magnitude grows with either mass. It falls rapidly as separation increases. Electrostatic force can attract or repel. Its sign depends on the product of both charges. Like charges repel. Unlike charges attract. Both mutual forces point along the separation line. Their paired values are equal in magnitude and opposite in direction.
Fields, Motion, and Resistance
External electric fields add force directly through charge times field. External magnetic fields act on moving charge. Magnetic force is perpendicular to both velocity and field. Therefore, it can change a path without changing speed in an ideal case. A uniform gravitational field adds weight. This calculator accepts its three components. You can model ordinary downward gravity or another specified acceleration field.
Quadratic drag represents resistance from a moving fluid. It depends on density, drag coefficient, reference area, and speed relative to the fluid. Drag always opposes relative motion. Set density, area, or drag coefficient to zero when drag does not apply. Manual external-force components support springs, thrust, contact forces, or measured loads. Enter a separate vector for each particle.
Net Force and Energy
The net force is the vector sum of every included contribution. Newton’s second law gives acceleration by dividing net force by mass. Acceleration predicts the instantaneous change in velocity. It does not automatically produce a complete path. Repeated time-step calculations are needed for trajectories. The displayed gravitational and electric potential energies describe the mutual pair only. External fields and manual forces may require additional potential-energy models.
Reliable Input Checks
Use consistent SI units for reliable output. Enter kilograms, coulombs, metres, seconds, volts per metre, tesla, and newtons. Very small charges or very large distances can create tiny values. Scientific notation is accepted. A zero charge receives no electric or magnetic field force. A zero velocity receives no magnetic or drag force. The particles must have different positions because zero separation makes mutual force undefined.
Interpret each component before relying on the final magnitude. Opposing forces can cancel along one axis while remaining large on another. Check the signs of coordinates and charges. Compare the force breakdown with your physical expectations. This is especially important when magnetic, drag, and manual forces act together. The calculator offers a detailed force snapshot. It supports analysis, verification, and structured physics practice.
Limits and Assumptions
The model assumes classical, nonrelativistic motion. It treats supplied electric and magnetic fields as external uniform fields. It does not calculate radiation reaction, nuclear forces, relativistic corrections, or detailed contact deformation. Apply specialized models when speeds approach light speed or materials experience complex interactions during collisions, chemical reactions, and deformation.
Frequently Asked Questions
1. Which forces does this calculator include?
It includes mutual gravity, mutual electrostatic force, external electric force, external magnetic force, uniform gravity, quadratic drag, and manual external force vectors.
2. Can two neutral particles attract here?
Yes. Neutral particles still experience mutual gravity when both masses are positive. Their electrostatic, electric-field, and magnetic-field forces become zero when both charges are zero.
3. Why must the particle positions differ?
The gravity and electrostatic equations divide by separation squared. A zero separation creates an undefined ideal point-particle force. Use a more detailed physical model for overlapping objects.
4. Does magnetic force change particle speed?
An ideal magnetic force is perpendicular to velocity. It changes direction, not kinetic energy. Other forces, such as electric fields or drag, can still change speed.
5. What sign should I enter for charge?
Use positive values for positive charge and negative values for negative charge. The charge signs determine whether the mutual electrostatic contribution is attractive or repulsive.
6. When should I use drag inputs?
Use them for motion through air, water, or another fluid when quadratic drag is suitable. Leave density, reference area, or drag coefficient at zero to exclude drag.
7. What does fluid velocity mean?
Fluid velocity is the local velocity of air or liquid. Drag depends on particle velocity relative to that fluid, not simply the velocity measured from the ground.
8. Can I add a spring force?
Yes. Calculate the spring vector separately, then place its x, y, and z components in the manual external-force inputs for the affected particle.
9. Are the output vectors in newtons?
Every force vector and force magnitude is in newtons. Acceleration vectors use metres per second squared. Pair potential energies are reported in joules.
10. Does this trace a full trajectory?
No. It calculates forces and instantaneous accelerations at one state. A trajectory requires updating positions and velocities over time with a numerical integration method.
11. Can this replace a relativistic particle model?
No. This calculator uses classical equations. Use relativistic electrodynamics or specialized simulation software when speeds approach the speed of light or field conditions become extreme.