🧲 Lorentz Force — Charged Particle in EM Fields

A charged particle in combined electric and magnetic fields obeys F = q(E + v×B). Pure B causes circular (cyclotron) motion; add E to produce cycloids and E×B drift. Drag the canvas to start the particle from any position.

Scenario

Fields

B field (out of page) 2.0 T E_x field 0.0 V/m E_y field 0.0 V/m

Particle

Charge q +1 e Mass m 1.0 u Initial v_x 3.0 Initial v_y 0.0

Stats

Larmor radius r_L—

Cyclotron freq ω_c—

E×B drift v_d—

Speed |v|—

What this simulation shows

In a uniform magnetic field B (pointing out of the screen), a charged particle moves in a circle — the cyclotron orbit. The radius r_L = mv/(|q|B) is the Larmor radius. Reversing the charge reverses the rotation direction.

Adding a perpendicular electric field E causes the particle to drift sideways at v_d = E/B — the E×B drift. This drift is independent of charge sign. In the cycloid scenario, the particle is launched from rest and rolls like a wheel along the field direction.

Did you know?

The Lorentz force is the operating principle behind mass spectrometers, the aurora borealis, and particle accelerators like the Large Hadron Collider. The LHC uses thousands of superconducting magnets to bend 7 TeV protons around a 27 km ring.