Lorentz Force Calculator (Charge in a Magnetic Field)
Enter the charge, speed, field strength and angle.
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Lorentz Force Calculator (Charge in a Magnetic Field) by TheCalcTools
How the Lorentz Force Calculator (Charge in a Magnetic Field) works
A charge moving through a magnetic field feels a force perpendicular to both its velocity and the field, of size qvB sin θ. Because the force is always sideways, it bends the path into a circle (or a helix) without changing the speed.
The radius is r = mv⊥ ÷ (qB) and the time per circle 2πm ÷ (qB), independent of speed. Mass spectrometers and cyclotrons use this.
The formula
Worked example
Using the default values shown in the calculator:
| Charge (C) | 1.60218e-19 |
|---|---|
| Speed (m/s) | 2e+06 |
| Magnetic field (T) | 0.5 |
| Angle between velocity and field (degrees) | 90 |
| Particle mass (kg, for the path radius) | 1.67262e-27 |
- A proton at 2,000 km/s across a 0.5 T field feels 1.60218e-13 N.
- It circles with radius 0.0418 m.
Result:
| Force (N) | 1.60218e-13 |
|---|---|
| Radius of the circular path (m) | 0.0418 |
| Period of one circle (ns) | 131.1889 |
| Cyclotron frequency (MHz) | 7.6226 |
Frequently asked questions
Which way does the force point?
Use the right-hand rule for positive charges (fingers along v, curl toward B, thumb gives F); it reverses for negative charges.
Sources and further reading
- Wikipedia: Lorentz force
- NIST CODATA: Fundamental physical constants
- HyperPhysics (Georgia State University)
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.