Lorentz Force Calculator
Calculate the magnetic and electric force on a moving charged particle using the Lorentz force law F = q(E + v×B).
Lorentz Force
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.