Lorentz Force Calculator

The Lorentz force is the magnetic force on a point charge q moving with velocity v in a magnetic field B: F⃗ = q(v⃗ × B⃗). The cross product means F is perpendicular to both v and B. Magnitude F = |q|vB sin θ, where θ is the angle between v and B. The most important case for circular motion is θ = 90°, giving F = |q|vB.

Direction is found with the right-hand rule for positive charge: point thumb along v, curl fingers toward B — palm pushes in the direction of F. Electrons (q < 0) curve the opposite way. In a uniform B field with v ⊥ B, the particle moves in a circle of radius r = mv/(|q|B) because qvB supplies centripetal force mv²/r.

Crucially, magnetic force does no work on the particle because F ⊥ v at every instant (W = ∫F·v dt = 0). Speed |v| stays constant in a pure magnetic field; only direction changes. If v has a component parallel to B, the path is a helix: circular motion in the perpendicular plane plus uniform drift along B.

The full electromagnetic Lorentz force includes the electric part: F⃗ = q(E⃗ + v⃗ × B⃗). Velocity selectors in mass spectrometers use crossed E and B so only particles with v = E/B pass straight through; all others are deflected.

Typical magnitudes: an electron (|q| = 1.6×10⁻¹⁹ C) at v = 10⁶ m/s in B = 0.5 T feels F ≈ 8×10⁻¹⁴ N — small but enough for tight curvature in particle detectors. Earth's field (~50 μT) gently steers cosmic rays; auroras come from charged solar wind in the magnetosphere.

Class 12 NCERT Moving Charges and Magnetism covers Lorentz force, circular motion in B, and cyclotron frequency ω = |q|B/m. JEE problems often combine energy conservation (electric) with magnetic deflection.