alleryAn electron and a proton enter a magnetic field with the same kinetic energy, perpendicular to B. The ratio of radii r_e / r_p is:
A1
Bm_p / m_e
C√(m_e / m_p)
D√(m_p / m_e)
Answer & Solution
Correct answer: C. √(m_e / m_p)
1. r = m v / (q B) = √(2 m K) / (q B), since p = √(2 m K).
2. r_e / r_p = √(m_e / m_p) (charges equal in magnitude).
3. So the lighter electron traces a SMALLER circle at the same KE.
_Source: syllabus Physics Ch 4 §4.3 (cyclotron radius scaling)_
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