# Consider the electromagnetic wave shown in the figure...

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Version 010 – Midterm 3 2PM Sp16 – yeazell – (55745) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Consider the electromagnetic wave shown in the figure below. B E In which direction is the wave propagating and how are the amplitudes E and B related? Suppose optical radiation (of wavelength 6 . 4 × 10 7 m) is used to determine the po- sition of an electron to within the wavelength of the light. What will be the minimum resulting uncer- tainty in the electron’s velocity? The mass of an electron is 9 . 10939 × 10 31 kg and Planck’s constant is 6 . 62607 × 10 34 J · s. Use Heisenberg’s Uncertainty principle, Δ p Δ x h 4 π 1. 85.1233 2. 128.631 3. 144.71 4. 76.1629 5. 192.946 6. 160.788 7. 99.7997 8. 90.4435 9. 120.591 10. 180.887 1. it is not propagating; E = cB 2. it is not propagating; E = B/c 3. traveling to the right; E = cB 4. traveling to the left; E = B/c 5. traveling to the right; E = B/c Correct answer: 90 . 4435 m / s. drawn). Then vector E × vector B is along the negative z axis. Therefore, the electromagnetic wave is traveling to the left. 002 10.0points
6. traveling to the left; E = cB correct Explanation: The vector E vector and vector B vector are not at the same point on the velocity axis. Pick an instant in time, where the B and E fields are at the same point on the velocity axis. v z y x B E For instance, let us choose the point where the vector B vector is along the y axis, as shown in the above figures. At this same instant, the vector E vector is along the negative x axis (at a point with a phase difference of 360 from the place on the velocity ( z ) axis where the vector B vector is Explanation: Let : Δ x = 6 . 4 × 10 7 m , h = 6 . 62607 × 10 34 J · s , and m = 9 . 10939 × 10 31 kg . Δ v h 4 π m Δ x = 6 . 62607 × 10 34 J · s 4 π (9 . 10939 × 10 31 kg) × 1 (6 . 4 × 10 7 m) = 90 . 4435 m / s . 003 10.0points
Version 010 – Midterm 3 2PM Sp16 – yeazell – (55745)