A charge moving across a magnetic field feels a force F = BQv sinθ, always at right angles to its velocity. That perpendicular force does no work and bends the path into a circle of radius r = mv / BQ. Add an electric field and you can build a velocity selector that lets just one speed through.
MissionIn the magnetic field, predict how the radius of the circular path changes when the speed is doubled.Streak 0Best 0
In a fixed magnetic field, doubling the speed of the charge changes the radius of its path to:
modemagnetic field
speed v , flux density B5 ×10⁶ m/s , 5 mT
radius r = mv/BQ5.7 mm
The magnetic force is always perpendicular to the velocity, so it changes direction but not speed: the path is a circle.