VELOCITY SELECTOR
Crossed E⊥B pass exactly one speed: v = E/B, with no q and no m in the verdict.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Two charged plates make an electric field pointing one way; a magnetic field threads the same region into the page. A charged beam runs the gauntlet between them. The electric force is fixed; the magnetic force grows with speed — so somewhere, exactly one speed balances.
The gate
q E equals q v B when v equals E over B — and notice the charge cancels out of its own verdict. The selected speed contains no q and no m: electrons, protons, and heavy ions all face the same gate. That absence is the entire instrument.
The force ledger
Off the gate, the net force is q times E minus v B, and its direction is honest: too slow and the electric force wins, bending the beam toward E; too fast and the magnetic force wins, bending it away. Downstream, a slit passes only the straight survivors — and that filtered v is exactly what the mass spectrometer takes as given.
Crossing the gate
The sweep runs the beam speed from well below the gate to well above: the bend flattens, vanishes at exactly E over B, and reverses sign. One zero crossing, no second chances — a comparator built out of fields.
Audit
Audited: at the defaults the balance q E minus q v-sel B is exactly zero — residual 0.0 — for the proton, the deuteron, and the alpha alike; the selected speed computes identically for all three because charge and mass never enter the formula; the deflecting force is 3.20435 femtonewtons toward E at eighty percent of the gate speed, sign-flipped above it; and the verdict is a strict float equality — one slider step off fails, no tolerance smuggled in.