All Problems Motion of Charged Particles in Electric and Magnetic Fields
Problem 3.407
The magnetic induction in a betatron on an equilibrium orbit of radius \(r\) varies during the acceleration time at practically constant rate from zero to \(B\). Assuming the initial velocity of the electron to be equal to zero, find: (a) the energy acquired by the electron during the acceleration time; (b) the corresponding distance covered by the electron if the acceleration time is equal to \(\Delta t\)
(a) \(W=\left(\sqrt{1+\left(r e B / m_{0} c\right)^{2}}-1\right) m_{0} c^{2}\) (b) \(s=W \Delta t / r e B\).