AAPT UNITEDSTATES PHYSICS TEAM AIP 2007 b.Diamagnetism. We model a diamagnetic substance to have all atoms oriented so that the electron orbits are in the x-y plane,exactly half of which are clockwise and half counterclockwise when viewed from the positive z axis looking toward the origin.Some substances are predominantly diamagnetic. (3 pts)i.Calculate the total magnetic moment of a diamagnetic substance with N atoms. Write your answer in terms of any or all of the following parameters: e,m,R,N,and uo. (6 pts)ii.An external magnetic field Bo=Bo2 is applied to the substance.Assume that the introduction of the external field doesn't change the fact that the electron moves in a circular orbit of radius R.Determine Ao,the change in angular velocity of the electron,for both the clockwise and counterclockwise orbits.Throughout this entire problem you can assume that A<.Write your answer in terms of e,m.,andB。only. (6 pts)iii.Assume that the external field is turned on at a constant rate in a time interval At. That is to say,when t=0the external field is zero and when t At the external field is B.Determine the induced emf experienced by the electron.Write your answer in terms of any or all of the following parameters:e,m,R,N,Bo,@o,and Lo- (6 pts)iv.Verify that the change in the kinetic energy of the electron satisfies AK=e8. This justifies our assumption in(ii)that R does not change. (6 pts)v.Determine the change in the total magnetic moment Am for the N atoms when the external field is applied,writing your answer in terms of e,m,R,N,uo and Bo. (3 pts)vi.Suppose that the uniform magnetic field used in the previous parts of this problem is replaced with a bar magnet.Would the diamagnetic substance be attracted or repelled by the bar magnet?How does your answer show this? Copyright C 2007,American Association of Physics TeachersCopyright © 2007, American Association of Physics Teachers , b. Diamagnetism. We model a diamagnetic substance to have all atoms oriented so that the electron orbits are in the x-y plane, exactly half of which are clockwise and half counterclockwise when viewed from the positive z axis looking toward the origin. Some substances are predominantly diamagnetic. (3 pts) i. Calculate the total magnetic moment of a diamagnetic substance with N atoms. Write your answer in terms of any or all of the following parameters: , ,, and e em RN 0 μ . (6 pts) ii. An external magnetic field 0 0 B = B zˆ G is applied to the substance. Assume that the introduction of the external field doesn’t change the fact that the electron moves in a circular orbit of radius R. Determine Δω , the change in angular velocity of the electron, for both the clockwise and counterclockwise orbits. Throughout this entire problem you can assume that Δω  ω0 . Write your answer in terms of e m, e , and B0 only. (6 pts) iii. Assume that the external field is turned on at a constant rate in a time interval Δt . That is to say, when t = 0 the external field is zero and when the external field is t = Δt 0 B . G Determine the induced emf E experienced by the electron. Write your answer in terms of any or all of the following parameters: , , , , e em RN B0 , ω0 , and 0 μ . (6 pts) iv. Verify that the change in the kinetic energy of the electron satisfies E. This justifies our assumption in (ii) that R does not change. Δ = K e (6 pts) v. Determine the change in the total magnetic moment Δm for the N atoms when the external field is applied, writing your answer in terms of 0 , ,, , e em RN μ and 0 B . (3 pts) vi. Suppose that the uniform magnetic field used in the previous parts of this problem is replaced with a bar magnet. Would the diamagnetic substance be attracted or repelled by the bar magnet? How does your answer show this?