Charged particle in electric & magnetic fields
A moving charge in a magnetic field feels F = qv×B — a force that's always at right angles to its velocity. That single fact is why the path bends into a perfect circle instead of speeding up or slowing down. Pick a particle, set the field, and watch it curve. Then switch to the velocity selector and find the one speed that slips through undeflected.
The physics you're seeing
The magnetic force
F = qv×B is always perpendicular to velocity, so it changes direction but never speed — that's why the path is a circle, not a spiral.
Radius depends on momentum
r = mv/(qB): faster or heavier particles trace bigger circles; a stronger field B shrinks the circle.
Cyclotron period is speed-independent
T = 2πm/(qB) doesn't depend on v or r at all — this is the whole trick behind how a cyclotron accelerator works.
Velocity selector
Only particles with v = E/B pass through undeflected, regardless of their mass or charge magnitude — used to filter a beam to one exact speed.
Part of the Moving Charges and Magnetism chapter — read the notes, grab the formula sheet and take the quiz. One of Priodemy for School, free with every EduSuite school.
Why the path is a circle
A force that never does work
The magnetic force on a moving charge is F = qv × B. The cross product means the force is perpendicular to the velocity at every instant — and a force perpendicular to motion can change direction but never speed. No work is done on the particle, its kinetic energy is constant, and the result is uniform circular motion. This is the single idea the whole simulation is built to show.
Contrast that with an electric field, where F = qE acts along the field regardless of how the particle is moving. An electric field speeds a charge up or slows it down; a magnetic field only steers it. Switch between the two here and the difference is immediate: one changes the speed readout, the other leaves it untouched while bending the path.
The radius, and what it depends on
Setting the magnetic force equal to the centripetal force needed, qvB = mv²/r, and cancelling one factor of v gives r = mv/qB. Since mv is the momentum p, the radius is simply r = p/qB — the radius measures momentum, which is exactly how particle detectors identify what passed through them.
Raise the field strength and the circle tightens, because B is in the denominator. Raise the speed and it widens. Increase the mass and it widens too, which is why a proton traces a much larger circle than an electron at the same speed in the same field.
The period that ignores speed
The time for one full circle is T = 2πm/qB. The speed has cancelled out entirely. A fast particle travels a bigger circle but covers it proportionally faster, so it takes exactly as long as a slow one. This is not a curiosity — it is the operating principle of the cyclotron, which can apply an accelerating voltage at a fixed frequency because the particles keep returning on schedule no matter how much energy they have gained.
The velocity selector
Cross an electric field with a magnetic field so that the electric force qE and the magnetic force qvB oppose each other. They balance only when qE = qvB, that is when v = E/B. Particles at exactly that speed pass straight through undeflected; anything faster or slower is bent aside. The charge cancels, so the selected speed is the same for every particle regardless of charge or mass.
Mistakes that cost marks
Assuming a magnetic field always deflects a charge. It does nothing to a stationary charge, and nothing to one moving parallel to the field, because the cross product is zero in both cases. A charge moving at an angle to the field traces a helix, not a circle.
Getting the direction wrong. Use a consistent rule and remember that for a negative charge the force is opposite to what the right hand gives for a positive one. Electrons circulate the other way round, and a diagram drawn with the wrong sense loses marks even when the arithmetic is right.
Claiming the magnetic field changes the particle's energy. It cannot. If a question asks about a change in speed or kinetic energy, the answer must involve an electric field or some other force — never the magnetic one alone.