| Cue Column | Notes Column |
|---|---|
| Why circular path? | Magnetic force F = qvB is always ⊥ to v → centripetal force; no work done |
| Radius of circular path | r = mv/(qB); [r] = [M·$LT^{-1}$ / A·T·$MT^{-2}$$A^{-1}$] = [L] = m |
| Time period | T = 2πm/(qB); depends only on m, q, B — NOT on velocity or radius |
| Cyclotron frequency | f = qB/(2πm); used in cyclotron particle accelerators |
| Helical path condition | Component v_∥ along B → no force; component v_⊥ to B → circular; net = helix |
| Pitch of helix | p = v_∥ × T = v cosθ × (2πm/qB) |
| Proton vs alpha in same field | r_p = m_pv/(eB); r_α = 4m_pv/(2eB) = 2r_p; alpha has twice the radius |
| Velocity selector | When qE = qvB: v = E/B; selects particles of specific speed |
**Summary:** A charge moving perpendicular to B traces a perfect circle (no work done by B). The cyclotron period is uniquely independent of speed — this is the key NEET insight. If velocity has a component along B, the path becomes helical. The pitch equals v_∥ × T.$
Part of MAG-01 — Magnetic Effects of Current & Magnetism
Cornell Notes — Subtopic: Circular Motion of Charged Particles in Magnetic Fields
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