Suppose that you have an electron moving with speed comparable to the speed of light in a circular orbit of radius r in a large region of uniform magnetic field B. (a) What must be the relativistic...

Suppose that you have an electron moving with speed comparable to the speed of light in a circular orbit of radius r in a

large region of uniform magnetic field B.

(a) What must be the relativistic momentum p of the electron?

(b) Now the uniform magnetic field begins to increase with time: , where and b are positive constants.

In one orbit, how much does the energy of the electron increase, assuming that in one orbit the radius doesn't

change very much? (This effect was exploited in the “betatron,” an electron accelerator invented in the 1940s.)

Note: It turns out that the electron's energy increases by less than the amount you calculated, for reasons that will become

clear in Chapter 24.