A charged particle q enters a uniform magnetic field B with velocity v perpendicular to B. What is the radius of its circular trajectory?
Answer and explanation
Correct answer: D. r = mv / (qB)
- Step 1: The magnetic Lorentz force acts perpendicular to velocity, providing centripetal force: qvB = mv^2 / r. Step 2. Cancelling one factor of v and solving for r gives r = mv / (qB) = p / (qB). *Answer: r = mv / (qB). Why not the others:* Trajectory radius is directly proportional to momentum and inversely proportional to charge and field.
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