A coupled physical and energy argument
An ideal classical particle with charge q and mass m enters a spatially uniform constant magnetic field B. Its velocity has both parallel and perpendicular components, and no electric field, radiation loss, collision or relativistic correction is included in the supplied model. A learner argues that a changing velocity direction necessarily means the magnetic field adds kinetic energy. Another treats the whole velocity as perpendicular and predicts a circle rather than a helix. The task is to use the vector force and the separate components, identify the work rate and describe which model changes would require a new analysis. No real beam device, hazardous apparatus or operating procedure is described.
1. Does the magnetic force change kinetic energy here?
Read the worked answer
The force is qv×B, perpendicular to v, so instantaneous power F·vis zero. Speed and kinetic energy remain constant in this ideal model.
2. What path follows from the components?
Read the worked answer
The perpendicular motion is circular and the parallel component remains uniform, giving a helix when both components are nonzero. Additional fields, losses or relativistic momentum would change the analysis.