cyclotron motion
/ SY-kloh-tron /
Cyclotron motion is the circular (or corkscrew-shaped) path a charged particle follows when it moves through a magnetic field. Fire an electron sideways into a uniform field and instead of flying straight it loops around and around in a circle. This is what traps charged particles in the Van Allen belts around the Earth and what a cyclotron uses to whirl protons up to high energy. It answers, what motion does the Lorentz force actually produce?
Because the magnetic force is always perpendicular to the velocity, it acts exactly like a centripetal force, forever turning the particle toward a center without changing its speed. Setting the magnetic force equal to the mass-times-centripetal-acceleration gives q v B = m v^2 / r, so the radius of the circle is r = m v / (q B). A faster or heavier particle makes a bigger circle; a stronger field makes a tighter one. If the particle also has some velocity along the field, that part is unaffected, and the overall path becomes a helix (a stretched spring shape) rather than a flat circle.
This motion is the basis of many tools: mass spectrometers separate ions by the size of their circular paths, cyclotrons and synchrotrons accelerate particles, and plasma confinement in fusion research relies on magnetic fields making charged particles spiral rather than escape. The speed, and hence the kinetic energy, stays fixed because the magnetic force does no work.
A proton of speed v in a field B travels a circle of radius r = m v / (q B). Double the field strength and the circle shrinks to half its radius; the proton curls twice as tightly.
Radius r = m v / (q B): stronger field, tighter loop; faster particle, wider loop.
The speed and kinetic energy stay constant during pure cyclotron motion, because a magnetic force does no work; only the direction of the velocity keeps changing.