Velocity Selector — Crossed E×B Fields

Fields

Electric field E 4.0

Magnetic field B 2.0

Launch speed v₀ 2.0

Readout

Traveling…

Drift speed E/B

2.00

Speed mismatch

0.00

Lateral force F_y

0.00

Particle vy

0.00

How it works

A charged particle in combined electric and magnetic fields feels the Lorentz force:

F = qE + qv × B

Here E points vertically between the plates (ŷ) and B points through the gap along the depth axis (ẑ), so a particle moving along x with speed v_x feels a vertical force

F_y = q(E − v_x·B)

That force vanishes — and the particle sails straight through the exit slit — only when

v_x = E / B   (the "selected" velocity)

Any other launch speed leaves a net F_y, which curves the path; since a sideways velocity then also feels the magnetic term, the trajectory bends into an arc rather than a straight line, and the particle is blocked by the slit or absorbed by a plate. This exact device — a velocity selector or Wien filter — is used in mass spectrometers and electron-beam instruments to pass only particles of one chosen speed regardless of their charge or mass.

E / B sliders — set the field strengths (arbitrary simulation units).
v₀ slider — the particle's launch speed along the beam axis.
Charge ± — flips the sign of q; the equilibrium condition v = E/B does not depend on charge sign, only its magnitude does not matter either — only the ratio of fields does.
Set v₀ = E/B — snaps the launch speed to the exact selected value so you can see the straight-through case.

Charged particle E field (plates) B field (depth axis)

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