A charged particle moves in a uniform field B such that its velocity has a component v∥ parallel to B. The distance moved along the field in one full revolution (the pitch) is:
A2πmv∥ / (qB)
B2πmv / (qB)
Cmv∥ / (qB)
Dπmv∥ / (qB)
Answer & Solution
Correct answer: A. 2πmv∥ / (qB)
1. The parallel velocity component $v_\parallel$ is unaffected by the field, giving helical motion.
2. The pitch is the axial distance per revolution: $p = v_\parallel T$.
3. The period is $T = \dfrac{2\pi m}{qB}$.
4. Therefore $p = v_\parallel \times \dfrac{2\pi m}{qB} = \dfrac{2\pi m v_\parallel}{qB}$.
_Source: syllabus Physics Ch 4 "Moving Charges and Magnetism", p.140_
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