Calculator Inputs
Positive signed force means repulsion along your chosen axis. Negative signed force means attraction along that same axis.
Formula Used
Lorentz force: F = q(E + v × B)
Magnetic magnitude: FB = |q|vBsin(θ)
Electric axis component: FE,axis = qEcos(φ)
Net axis force: Faxis = FE,axis + direction × FB
Parallel wire force: F = μ₀I₁I₂L / (2πr)
Coulomb force: F = kq₁q₂ / r²
Here q is charge. E is electric field. v is velocity. B is magnetic flux density. θ is the angle between velocity and magnetic field. φ is the projection angle to the repulsion axis.
How to Use This Calculator
- Enter the particle charge and choose its sign.
- Enter electric field strength and its axis angle.
- Enter velocity, magnetic field, and the velocity-field angle.
- Select whether magnetic force is repulsive, attractive, or sideways.
- Add particle mass if acceleration is needed.
- Use the wire and point charge sections when those models apply.
- Press the calculate button and read the result above the form.
Understanding Lorentz Repulsion
Electromagnetic repulsion appears when fields push charge, current, or charged matter away from a chosen axis. The Lorentz force gives a compact model for this effect. It joins electric force and magnetic force in one relation. The electric part depends on charge and field strength. The magnetic part depends on charge, speed, magnetic flux density, and angle.
This calculator keeps those parts visible. It does not hide the sign of the answer. A positive signed result means repulsion along your selected axis. A negative value means attraction or pull along that axis. This matters in particle beams, motors, rails, plasma devices, and magnetic separators.
Why Direction Matters
Magnitude alone can mislead. Magnetic force is not always aligned with motion. It is perpendicular to velocity and magnetic field. The sine of the angle controls its strength. A charge moving parallel to a magnetic field has no magnetic Lorentz force. A charge moving at ninety degrees has maximum magnetic force.
The electric component uses a projection angle. That angle tells how much of the electric force lies on the repulsion axis. The magnetic direction option lets you apply the right hand rule. Use it after deciding whether the magnetic force points outward, inward, or sideways.
Advanced Use Cases
The charged particle fields are useful for ion optics and mass analysis. The acceleration result helps estimate particle response when mass is known. The wire current model uses the long parallel conductor relation. Opposite currents repel. Same direction currents attract. This is important in busbars and pulse power conductors.
The charge pair model adds Coulomb force. It is helpful when electric repulsion between two point charges dominates. Real devices may need edge correction, shielding, finite conductor size, and field maps. Still, these equations give a strong first estimate for design checks.
Reading the Output
The result panel separates electric, magnetic, wire, and Coulomb forces. It also reports a combined signed index. Use that combined value only when your entered systems act on the same body and along the same axis. Otherwise, read each line as a separate scenario.
For high accuracy, enter SI units or choose the matching unit menu. Keep angles in degrees. Use measured field data when available. Round final answers to match your instruments. For safety work, add margin. Strong fields, high currents, and fast particles can create serious hazards.
Limits and Assumptions
The tool assumes steady fields and simple geometry. It treats particle motion with one speed and one angle. It treats long wires as straight and parallel. It treats point charges as very small compared with their spacing. These assumptions are common for first pass work. They are not a replacement for laboratory tests or detailed simulation.
When fields change quickly, induction and radiation may matter. When speeds approach light speed, relativistic terms become important. Use the output as a practical screening value before final modeling.
Example Data Table
| Scenario | Main Inputs | Expected Trend | Useful Output |
|---|---|---|---|
| Positive ion in electric field | q = 1 uC, E = 5000 V/m | Repulsive if field points outward | Electric force component |
| Fast charge in magnetic field | v = 1000 m/s, B = 0.02 T, θ = 90° | Maximum magnetic term | Magnetic Lorentz force |
| Opposite busbar currents | I₁ = 500 A, I₂ = 500 A, r = 2 cm | Repulsion between conductors | Wire force and force per meter |
| Two like point charges | q₁ = 2 uC, q₂ = 2 uC, r = 10 cm | Electric repulsion | Coulomb force |
FAQs
1. What does a positive force mean?
A positive signed force means the net component points along your chosen repulsion axis. It is not always the total vector magnitude. It is the useful outward component for your selected direction.
2. What does a negative result mean?
A negative value means the selected force component acts inward. It shows attraction along the chosen axis. Check charge sign, electric field direction, and magnetic direction settings.
3. Why is the magnetic term zero sometimes?
The magnetic part is proportional to sin(θ). If the particle moves parallel to the magnetic field, θ is zero. The sine is zero, so magnetic force is zero.
4. Can electric field and magnetic field forces cancel?
Yes. Their components can point in opposite directions. The calculator adds signed components on the repulsion axis, so cancellation appears as a smaller net Lorentz force.
5. How should I choose magnetic force direction?
Use the right hand rule for a positive charge. Reverse the direction for a negative charge. Then choose repulsive, attractive, or sideways based on your selected axis.
6. Does this handle relativistic particles?
It gives a classical estimate. When speed is a large fraction of light speed, relativistic corrections may be needed. Treat those results as screening values only.
7. Why include the parallel wire model?
Current-carrying conductors can repel or attract because each wire sits in the magnetic field of the other. Opposite current directions repel. Same directions attract.
8. Is Coulomb force the same as Lorentz force?
Coulomb force is the electric interaction between charges. It is consistent with the electric part of electromagnetic force. The Lorentz expression also includes magnetic effects from moving charges.
9. What units should I use?
The calculator converts common units to SI internally. You can enter microcoulombs, millitesla, centimeters, and other listed units. Results are shown mainly in newtons.
10. Can I use this for motor design?
It can support early checks and learning. Real motor design needs geometry, coil turns, saturation, air gap details, losses, and finite element analysis for accurate results.
11. Why is the combined index optional?
The combined index adds different modeled forces. Use it only when all entered effects act on the same body and same axis. Otherwise, compare the separate outputs.