A velocity selector is a region with perpendicular (crossed) electric and magnetic fields arranged so the electric force and magnetic force on a charged particle cancel. Only particles moving at exactly v = E/B travel through undeflected, because that's the speed where qE = qvB.
A velocity selector is a setup where a uniform electric field and a uniform magnetic field point perpendicular to each other, and a charged particle shoots through perpendicular to both. The electric field pushes the charge one way with force F_E = qE. The magnetic field pushes it the other way with force F_B = qvB sin θ (and since the velocity is perpendicular to B, sin θ = 1, so F_B = qvB). If those two forces are equal and opposite, the net force is zero and the particle sails through in a straight line.
Here's the trick that gives the device its name. The electric force doesn't care how fast the particle moves, but the magnetic force does. So there's exactly one speed where the forces balance. Set qE = qvB, cancel the charge, and you get v = E/B. Anything faster gets bent one way (magnetic force wins), anything slower gets bent the other way (electric force wins). Notice that q dropped out of the equation. The selector filters by speed, not by charge or mass, which is exactly why mass spectrometers use one as the front door.
The velocity selector lives in Topic 12.2 (Magnetism and Moving Charges) in Unit 12 of AP Physics 2. It directly supports learning objective 12.2.B, describing the force a magnetic field exerts on a moving charge, and it forces you to use the right-hand rule and F_B = qvB sin θ in the same breath as Coulomb-style electric forces from earlier units. It's also the single best example of a 'balanced forces' argument in electromagnetism. Instead of memorizing a gadget, you're applying Newton's first law to a charged particle, which is the kind of reasoning AP Physics 2 rewards everywhere.
Keep studying AP® Physics 2 Unit 12
F_B = qvB sin θ (Unit 12)
The selector condition qE = qvB is just this equation set equal to the electric force. The whole device is one application of the magnetic force law with θ = 90°.
Charge-to-mass ratio and the mass spectrometer (Unit 12)
A mass spectrometer puts a velocity selector first so every ion enters the next region at the same known speed v = E/B. Then a magnetic field alone bends them into circles, and the radius reveals each ion's mass. Without the selector, you couldn't tell whether a wide circle meant a heavy ion or a fast one.
Circular motion and radius of curvature (Units 1 & 12)
Inside the selector the particle moves in a straight line because forces balance. The moment it exits into a B-field-only region, the unbalanced magnetic force becomes a centripetal force and the path curves into a circle with r = mv/(qB). Exam problems love chaining these two regions together.
Hall effect (Unit 12)
The Hall effect is the same physics happening inside a conductor. Moving charges get pushed sideways by a magnetic field until the charge buildup creates an electric field that balances the magnetic force. It's a velocity selector that builds its own E field.
Velocity selector questions show up mostly as multiple choice and as the setup phase of longer quantitative problems. The classic stem hands you E and B values and asks for the speed of an undeflected particle (v = E/B), or describes a charged particle in crossed fields and asks under what condition it travels in a straight line. Be ready to (1) state the balance condition qE = qvB and explain why charge cancels, (2) use the right-hand rule to figure out which way each force points and check that they actually oppose each other (watch the sign of the charge), and (3) predict what happens to a particle that's too fast or too slow. The most common multi-step version is the mass spectrometer problem, where ions pass the selector at v = E/B and then curve in a magnetic-field-only region, so you combine the selector equation with r = mv/(qB) to find mass or radius. No released FRQ has used the term verbatim, but the underlying skill, balancing electric and magnetic forces on a moving charge, is core LO 12.2.B territory.
Both involve an electric force balancing a magnetic force on moving charges, so the math looks identical. The difference is who sets up the fields. In a velocity selector, you impose external E and B fields, and only particles with v = E/B pass through. In the Hall effect, charges drifting in a conductor get pushed sideways by an external B field, pile up on one edge, and create their own internal E field that grows until it balances the magnetic force. The selector filters particles; the Hall effect measures fields or reveals the sign of charge carriers.
A velocity selector uses crossed (perpendicular) electric and magnetic fields so that the electric force qE and the magnetic force qvB cancel for one specific speed.
The selected speed is v = E/B, and charge cancels out of the equation, so the selector picks particles by speed regardless of their charge or mass.
Particles moving faster than E/B deflect toward the side where the magnetic force wins, and slower particles deflect the other way, because F_B depends on v but F_E does not.
Use the right-hand rule to confirm the magnetic force actually opposes the electric force, and remember to flip the magnetic force direction for negative charges.
In mass spectrometer problems, the velocity selector guarantees all ions enter the deflection region at the same speed, so the circular radius r = mv/(qB) sorts them by mass.
It's a region with perpendicular electric and magnetic fields tuned so the electric force (qE) and magnetic force (qvB) on a charged particle cancel. Only particles moving at exactly v = E/B pass through undeflected; everything else gets bent off course.
No. The condition qE = qvB has charge on both sides, so q cancels and v = E/B works for any charge or mass. Positive and negative particles both pass if they're at the right speed (the forces just swap directions for negative charges, but they still balance).
The velocity selector is the first stage of a mass spectrometer, not the whole thing. The selector lets only ions with v = E/B through; then a magnetic-field-only region bends those ions into circles with r = mv/(qB), and the different radii separate the masses.
If v > E/B, the magnetic force qvB exceeds the electric force qE and the particle deflects toward the magnetic-force side. If v < E/B, the electric force wins and it deflects the opposite way. Either way, it doesn't make it through the exit slit.
Set the forces equal, qE = qvB, and solve for v = E/B. For example, with E = 2.0 × 10^4 N/C and B = 0.50 T, the selected speed is 4.0 × 10^4 m/s.
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