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A) (B) (C) (D) (E) Unauthorized copying or reuse of any part of this page is illegal. 32 GO ON TO THE NEXT PAGE. SCRATCHWORK Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE. 33 41. Maxwell’s equations can be written in the form shown below. If magnetic charge exists and if it is conserved, which of these equations will have to be changed? I. ∇ ؒ E = r / ⑀o II. ∇ ؒ B = 0 III. ∇ × E = − ∂B ∂t IV. ∇ × B = µ o J + µ o⑀o (A) (B) (C) (D) (E) I only II only III only I and IV II and III ∂E ∂t 42.

2 (A) (B) (C) (D) (E) I only II only III only I and III II and III Unauthorized copying or reuse of any part of this page is illegal. 52 84. An energy-level diagram of the n = 1 and n = 2 levels of atomic hydrogen (including the effects of spin-orbit coupling and relativity) is shown in the figure above. Three transitions are labeled A, B, and C. Which of the transitions will be possible electric-dipole transitions? (A) (B) (C) (D) (E) B only C only A and C only B and C only A, B, and C GO ON TO THE NEXT PAGE.

51 80. A tube of water is traveling at 1/2 c relative to the lab frame when a beam of light traveling in the same direction as the tube enters it. What is the speed of light in the water relative to the lab frame? ) (A) (B) (C) (D) (E) 1/2 c 2/3 c 5/6 c 10/11 c c 81. Which of the following is the orbital angular momentum eigenfunction YAm (q , f ) in a state for which the operators L2 and Lz have eigenvalues 6= 2 and -=, respectively? (A) Y21 (q , f) (B) Y2-1 (q , f ) (C) (D) 1 [Y 1 (q , f ) + Y2-1 (q , f )] 2 2 Y32 (q , f) 83.

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