Chapter 29, Problem 55P

(II) The betatron, a device used to accelerate electrons to high energy, consists of a circular vacuum tube placed in a magnetic field (Fig. 29–48), into which electrons are injected. The electromagnet produces a field that (1) keeps the electrons in their circular orbit inside the tube, and (2) increases the speed of the electrons when B changes. (a) Explain how the electrons are accelerated. (See Fig. 29–48.) (b) In what directions are the electrons moving in Fig. 29–48 (give directions as if looking down from above)? (c) Should B increase or decrease to accelerate the electrons? (d) The magnetic field is actually 60 Hz ac; show that the electrons can be accelerated only during $\frac{1}{4}$ of a cycle $\left(\frac{1}{240}\text{s}\right)$. (During this time they make hundreds of thousands of revolutions and acquire very high energy.)