We showed that a particle of charge q and mass m will move in a circle of radius r = mv/|q|B when its velocity `vecv` is perpendicular to a uniform magnetic field `vecB`. We also found that the period T of the motion is independent of speed v. These two results are approximately correct it v << c. For relativistic speeds, we must use the correct equation for the radius:
`r=(p)/(|q|B)=(gamma mv)/(|q|B)`
(a) Using this equation and the definition of period `(T=2pi//v)`, find the correct expression for the period.
(b) Is T independent of v? If a 20.0 MeV electron moves in a circular path in a uniform magnetic field of magnitude 2.20 T, what are (c ) the radius according to , (d) the correct radius, (e ) the period according to, and (f) the correct period?

Answer

(a) `gamma(2pi m//|qB|)`; (b) no; (c ) 6.86 mm; (d) 3.12cm; (e ) 16.3 ps; (f) 652 ps