Question

since the period fo revolution of electrons in a unifrom magnetic field rapidly increases with the growth of energy, a cyclotron in unsuitable for their accelearation. This drawback is rectified in a microton (Fig) in which a change `Delta T` in the period of revolution of an electron is made multipile with the period of acclerating field `T_(0)`. How many times has an electron to cross the accerating gap of a microtron to acquire an energy `W = 4.6 MeV` if `Delta T = T_(0)` the magnetic induction is equal to `B = 107 mT`, and the frequency of accelerating field to `v = 3000 MHz` ?

Answer 1

In the nth oribit, `(2pi r_(n))/(v_(n)) = n T_(0) = (n)/(v)`. We igonre the rest mass of the electron and write `v_(n) = c`. Also `W = cp = cBer_(n)`.
Thus, `(2pi W)/(B ec^(2)) = (n)/(v)`
or, `n = (2pi W v)/(Be c^(2)) = 9`