An electron enters a uniform magnetic field B at angle θ to B with speed v. The pitch of its helical path is
- 2πm v sin θ / (eB)
- 2πm v cos θ / (eB)
- 2πm v / (eB)
- m v cos θ / (eB)
Show answer and solution
Correct answer: B. 2πm v cos θ / (eB)
1. Decompose velocity: parallel v∥ = v cos θ and perpendicular v⊥ = v sin θ.
2. The perpendicular component drives circular motion with period T = 2πm/(eB).
3. The parallel component moves the centre of the circle linearly at v cos θ.
4. Pitch = distance moved along the axis in one period = v cos θ · T = 2πm v cos θ/(eB).
_Source: syllabus Physics Ch 4 "Moving Charges and Magnetism", §4.3_