Circular Motion in Magnetic Field

Charged particle in uniform B traces a circle.

Concept

Circular Motion in Magnetic Field is a foundational idea in this chapter. The defining relationship is:

$r = mv/(qB), \quad T = 2\pi m/(qB)$

Period is independent of speed — basis of the cyclotron.

Worked Application

Apply the formula to a typical problem from your textbook. Identify the knowns, plug into the equation, and check that the units work out. Always sanity-check the magnitude before accepting an answer.

Common Confusions

• Confusing the variables in the formula — re-read the symbol definitions in the chapter.
• Forgetting unit conversions (cm vs m, g vs kg).
• Ignoring sign conventions where direction matters.

Key Takeaways

• Master the formula $r = mv/(qB), \quad T = 2\pi m/(qB)$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.