Problem 2

A positively charged particle of charge

q

and mass

m

enters a uniform magnetic field of magnitude

B

with velocity

v

perpendicular to the field. The field region is wide enough for a circular orbit; neglect gravity and relativistic effects. (a) Find the orbit radius and direction of turning. (b) Find the period and cyclotron angular frequency. (c) If the particle travels a circular arc of angle

\phi

(in radians) before leaving the field, find the time and arc length and explain how the time depends on

v

problems.proof.stepOf

problems.proof.prevStep problems.proof.nextStep

T=\frac{2\pi r}{v}=\frac{2\pi m}{qB},\qquad \omega=\frac{qB}{m}

problems.proof.analysis

One revolution covers $2\pi r$ at constant speed. Substituting the radius gives the period, whose reciprocal times $2\pi$ is angular frequency.