Please help

3 Questions

1.

In class we found that the magnitude of the magnetic field at the center of a ring with radius R and charge Q rotating about its axis in period T is B = MOQ 2RT . As a model of hydrogen's electronic current magnetic field, let Q = e (the elementary charge), R = 0.529A (the radius of hydrogen), and say the ring is rotating at the speed of an electron in hydrogen: v = 197 where c is the speed of light (see the top of the test for the parameters of this question). What is the magnitude of the magnetic field B (in tesla, the SI unit for magnetic field) at the center of this rotating ring? (Hint: remember, for an object rotating, v = RW = 2TR) TSimilar to the previous problem, a rotating charged ring, but now let's ask about the magnetic eld of a spinning electron itself. Model an electron as a charged ring rotating about its axis. But this time use the magnitude of the magnetic moment of an electron: M = 2:: (see the top of the test for the parameters of this question), and let the radius R of the ring be that of an electron from a recent experiment: R = 3.2 X 1019 meter. Recall as we showed in class, the magnetic eld at the center of a rotating ring can be written as _ HUM B 27ml?3 ' What is the magnitude of the magnetic eld B in tesla at the center of this rotating ring using M and R as just described? (Hint: Don't be shocked if this is an enormously large answer; R is very small here, so B is expected to be very big) Once again the magnetic eld of a spinning electron, but this time literally take the electron as a ring rotating at the speed of light. 50 this ti me use the formula like in problem 1: B = #0 2RT ' but now take R as the radius of an electron and let the ring be rotating at the speed of light; that is, use this formula for B just written with Q = e , R = 3.2 X 1019 meter, and v = c (recall the hint of problem 1). Then what is the magnetic eld B in tesla at the center of this rotating ring? (Hint: With such a small R again, expect the eld to be very big, but this time not as big as problem 2)