Lorentz Force Calculator
Calculate magnetic and electric force on a moving charged particle using F = q(E + v×B).
Enter charge, velocity, and field strengths to get Newtons.
The Lorentz force is the total force on a charged particle moving in electric and magnetic fields:
F = q(E + v × B)
The magnetic component (magnitude): |F_mag| = q|v||B|sin(θ)
The electric component: F_elec = qE
Where:
- F = Total force (Newtons, N)
- q = Particle charge (Coulombs, C)
- E = Electric field (N/C = V/m)
- v = Particle velocity (m/s)
- B = Magnetic field (Tesla, T)
- θ = Angle between v and B vectors
Key features of magnetic force:
- Always perpendicular to velocity → does no work → cannot change particle speed, only direction
- Causes circular/helical motion in a uniform magnetic field
- Radius of circular motion: r = mv/(qB) — the “cyclotron radius”
Practical applications:
- Mass spectrometers: Different ions curve differently in B field → mass measurement
- Cyclotrons: Particles are accelerated in spiral paths by combined E and B fields
- Cathode ray tubes: Electron beam steered by magnetic force (old TV technology)
- Aurora borealis: Solar wind particles spiral along Earth’s magnetic field lines to the poles
- MRI machines: Atomic nuclei precess in a strong magnetic field
Hall effect: In a conductor with current, moving charges experience magnetic force sideways → measurable Hall voltage. Used in Hall-effect sensors for current measurement and position sensing.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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