Electromagnetic Force Calculator
Two Forces, One Underlying Field
A charged particle feels a push from an electric field whether it's moving or not, but it only feels a magnetic force when it's in motion — and that magnetic push acts sideways, perpendicular to both its velocity and the field. Combined, these two effects make up the Lorentz force, the complete description of how electric and magnetic fields act on charge. This calculator handles all three cases: pure electric force, pure magnetic force, and the combined Lorentz force.
The Formulas
Magnetic force: F = q × v × B × sin(θ)
Lorentz force: F = qE + qvB × sin(θ)
q is the particle's charge, E is electric field strength, v is velocity, B is magnetic field strength, and θ is the angle between the velocity and magnetic field vectors — the magnetic term is maximized at θ = 90°, where velocity and field are perpendicular, and vanishes when they're parallel.
Where This Governs Real Systems
- Particle accelerators — magnetic fields steer charged particles around a ring using exactly this sideways magnetic force, while electric fields do the accelerating.
- Electric motors and generators — the force on current-carrying wires in a magnetic field (a direct extension of the v×B term) is what converts electrical energy to mechanical motion and back.
- Mass spectrometry — ions are deflected by known magnetic fields, and the resulting curved path reveals their mass-to-charge ratio.
- Cathode ray and electron-beam devices — electric fields accelerate electrons while magnetic fields steer or focus the beam.
Two Reference Calculations
A proton (charge 1.602×10&supminus;¹&sup9; C) moving at 2×10&sup6; m/s perpendicular to a 0.5 T magnetic field experiences:
A 2 µC charge sitting in a 5,000 V/m electric field feels a purely electric force of:
Note how much larger the electric force is here despite the smaller charge — the relative strength of each term depends entirely on the specific charge, speed, and field values involved.
How to Use This Calculator
- Choose a mode: Electric Force, Magnetic Force, or Lorentz Force (Combined).
- Enter the Charge q (C) — required for every mode.
- For Electric Force, enter Electric Field E (V/m).
- For Magnetic Force, enter Velocity v (m/s), Magnetic Field B (T), and the Angle between v and B (defaults to 90°).
- For Lorentz Force, enter all of the above: Electric Field, Velocity, Magnetic Field, and Angle.
- Select Calculate to see the resulting force in newtons along with the worked formula.
Related Calculations
For the force between two point charges rather than a charge in a field, see the Coulomb's Law Calculator, or compare against the much weaker gravitational pull between masses with the Gravitational Force Calculator.