Cyclotron
Faster and faster, yet every lap takes the same time.
Inside the D-shaped electrodes (dees), a charged particle moves in uniform circular motion and is accelerated by the electric field every time it crosses the gap between them. The cyclotron period T = 2πm/(qB) does not depend on speed, so an alternating voltage of fixed frequency stays in step and accelerates the particle on every crossing. The radius grows lap by lap until the particle is extracted at the edge of the dees: the maximum kinetic energy is determined only by the magnetic field and the dee radius, not by the accelerating voltage.
Kinetic energy vs. accelerations
Each gap crossing adds qU; at the dee edge the kinetic energy reaches its limit, regardless of the voltage.
Think about it
If the accelerating voltage is raised to 2 times its original value, will the protons' final kinetic energy increase?
No. The maximum kinetic energy Ekm = q²B²R²/(2m) does not depend on the voltage; doubling the voltage only halves the number of accelerations, so the protons leave sooner. To raise the energy, increase the magnetic field or the dee radius.
Model assumptionsAccelerating protons · Relativistic effects and time in the gap ignored · At most 16 half-turns drawn
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.