🧭 2D Lorentz Force — Charged Particle Drift

A flat-plane particle feels F = qE + qv×B, with B pointing straight out of the page and E lying in the plane. RK4-integrated each frame — the measured orbit radius and frequency are computed live from the trajectory and checked against the textbook formulas r = mv/(|q|B) and ω = |q|B/m.

F = qE + qv×B

Scenario

Fields

B (out of page) 1.5 T E_x 0.0 V/m E_y 0.0 V/m

Particle

Charge q +1 e Mass m 1.0 u Speed |v₀| 3.0

Theory vs measured

r theory—

r measured—

ω theory—

ω measured—

E×B drift v_d—

How this differs from the 3D Lorentz Force sim

This companion keeps the particle strictly in the plane of the page: B is a scalar pointing out of (or into) the screen, and E is a 2D vector inside the screen. There is no parallel-to-B velocity component and therefore no helix — instead this page focuses on precisely checking the two textbook numbers, radius and angular frequency, by measuring them directly from the simulated path (bounding-circle radius and the time between successive velocity-angle wraps) and comparing them live to r = mv/(|q|B) and ω = |q|B/m.