A charged particle enters a uniform magnetic field at an angle. How do I find its path?
Split velocity into v_parallel along B and v_perp across B.
Split velocity into v_parallel along B and v_perp across B. Magnetic force ignores v_parallel, so that component carries the particle uniformly along the field. The perpendicular component produces a circle of radius mv_perp/(|q|B). Combining uniform forward motion with circular motion gives a helix. Its pitch is v_parallel times the cyclotron period 2pi m/(|q|B).
Key point
Parallel velocity advances the helix; perpendicular velocity sets its radius.
Common mistake
using total velocity for both radius and pitch.
Memory tip
parallel travels, perpendicular turns.
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