Helical Motion and Pitch
In a uniform magnetic field, v_perp produces circular motion of radius mv_perp/(|q|B), while v_parallel is unchanged. The helix pitch is the parallel distance traveled in one cyclotron period.
Why this shows up in the exam
Calculating helical pitch · Separating radius and axial advance · Interpreting particle tracks at oblique incidence
Learn the idea
A velocity component across B makes a circle while the parallel component carries the circle forward into a helix. Split the launch velocity into two independent motions. The perpendicular part keeps turning, while the parallel part proceeds uniformly, so their combination wraps around the field direction.
🧠 Memory hook: Across B makes the circle; along B makes the pitch.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- r = m v_perp/(|q| B) — radius of the helical projection
- pitch = v_parallel T — advance along B during one revolution
- pitch = 2 pi m v_parallel/(|q| B) — pitch after substituting the cyclotron period
How to approach it
- 1Resolve v into parallel and perpendicular components
- 2Use v_perp for radius and v_parallel for advance
- 3Multiply v_parallel by one full period
Common slip-ups that cost marks
- •Using total speed in the radius
- •Using v_perp in the pitch
- •Calling an almost perpendicular path exactly circular when v_parallel is nonzero
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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