Question

Since the period of revolution of electrons in a uniform magnetic field rapidly increases with the growth of energy, a cyclotron is unsuitable for their acceleration. This drawback is rectified in a microtron (Fig. 3.105) in which a change ΔT in the period of revolution of an electron is made multiple with the period of accelerating field T₀. How many times has an electron to cross the accelerating gap of a microtron to acquire an energy W = 4.6 MeV if ΔT = T₀, the magnetic induction is equal to B = 107 mT, and the frequency of accelerating field to v = 3000 MHz?

Answer 1

In the nth orbit,  We ignore the rest mass of the electron and write