Suppose that you have an electron moving with speed comparable to the speed of light in a circular orbit of radiusrin a large region of uniform magnetic fieldBB. (a) What must be the relativistic momentumppof the electron? (Enter the magnitude. Use any variable or symbol stated above along with the following as necessary:e, for the charge of the electron.)

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(b) Now the uniform magnetic field begins to increase with time:B=B₀+bt, whereB₀andbare 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 23. (Use the following as necessary:e,b, andr.)

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