Problem 2
A particle of mass and charge moves perpendicular to a uniform magnetic field at speed . Find orbit radius and period; use for charge magnitude. The magnetic field is perpendicular to the initial velocity; neglect gravity and collisions. (a) Use the Lorentz force to find orbit radius . (b) Find the orbital period . (c) Find the cyclotron frequency and identify which result is independent of speed . Express each answer in terms of the supplied parameters, using SI units for any numerical evaluation. State the assumptions used, check dimensions at each result, and compare with the governing law to catch a sign error or a missing condition.
problems.proof.stepOf
problems.proof.analysis
The next equation adds the relevant constraint or conservation law. Without it, the variables would not be linked and the system could not be solved consistently.
problems.proof.pitfall. Do not omit the sign convention or the model’s physical condition; check the limiting case before accepting a solution.