Cyclotron Design -- Answer EITHER this question OR the one on the previous page OR the one on the next page!

1.

[6 marks] Show that the orbital period T of a charged particle moving perpendicular to a uniform magnetic field B is independent of the particle's velocity v as long as $v \ll c$ (where c is the speed of light).

2.

[6 marks] Show that when a particle of rest mass m is accelerated to kinetic energy K, its orbital period is multiplied by a factor ${\displaystyle \left( 1 + {K \over mc^2} \right) }$.