🎬The magnetic force does zero work on a particle undergoing cyclotron motion in a uniform magnetic

The magnetic force does zero work on a particle undergoing cyclotron motion in a uniform magnetic field

The animated demonstration vividly illustrates the core operational principles of the cyclotron accelerator. The top plot dynamically shows the particle's spiral trajectory, which directly visualizes the physics that the magnetic field does zero work; its only role is to apply a centripetal force that bends the particle's path. The outward spiraling is caused by the periodic energy boosts (simulating the electric field's work), which continuously increases the particle's speed, leading to a proportionally larger orbital radius ( $r \propto v$ ). The critical takeaway is demonstrated by the bottom plot: despite the increasing radius and speed, the time taken for each half-cycle remains constant and perfectly matches the theoretical cyclotron period ( $T / 2$ ). This time-independence is the "magic" that allows a constant-frequency alternating electric field to remain perpetually synchronized with the particle's motion, ensuring continuous, efficient acceleration.

🎬Narrated Video

🧵Related Derivation

🧄The Lorentz Force and the Principle of Zero Work Done by a Magnetic Field (LF-ZW-MF)

⚒️Compound Page

The magnetic force does zero work on a particle undergoing cyclotron motion in a uniform magnetic field | Resulmationviadean on Notion