# 033 part 1 of 2 100 points consider the passage of a

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033 (part 1 of 2) 10.0 points Consider the passage of a horizontal electron beam through a velocity selector, where the electric field vector E points downward and the mag- netic field vector B points into the paper. v E B Based on the Lorentz force law, what is the critical speed v c (the speed at which the horizontal electron beam is not deflected)? 1. v c = E B correct 2. v c = B E 2 3. v c = E 2 B 4. v c = B 2 E 5. v c = 1 B E 6. v c = B E 7. v c = E B 2 8. v c = B 2 E 9. v c = B E 10. v c = B E 2 Explanation: Consider the net effect of the electric force and the magnetic force which oppose each other. At the critical speed, the magnetic force is exactly canceled by the electric force, i.e. , the Lorentz force v B v B F = q v B μ vector F = q vector E + qvectorv × vector B = 0 q E = q v c B , so the critical speed is v c = E B . 034 (part 2 of 2) 10.0 points If the speed of the electrons is greater than the critical speed, the trajectory of the electron beam will be 1. deflected out of the paper. 2. deflected downward and into the paper. 3. deflected upward and into the paper. 4. deflected downward. correct 5. deflected upward. 6. deflected into the paper. 7. deflected upward and out of the paper. 8. undeflected.
Canter (zwc73) – Chapter 27: Magnetic Fields and Forces – Thompson – (0137) 14 9. deflected downward and out of the pa- per. Explanation: The magnetic force points downward. If v > v c , the magnetic force will be stronger, so the electron beam will be deflected downward. Thus the separation is d = 2 ( R 2 R 1 ) = 2 (2 . 44343 m 2 . 41263 m) = 0 . 061599 m = 6 . 1599 cm . 036 10.0 points
035 10.0 points A mass spectrometer is used to examine the isotopes of uranium. Ions in the beam emerge from the velocity selector at a speed of 4 . 2 × 10 5 m / s and enter a uniform magnetic field of 0 . 424 T directed perpendicularly to the velocity of the ions. The charge on the singly charged ion is 1 . 60218 × 10 19 C, and the atomic mass unit is 1 . 66054 × 10 27 kg. What is the distance between the impact points formed on the photographic plate by singly charged ions of 235 U and 238 U ? In a mass spectrometer, ions are directed into a magnetic field, where they curve around a magnetic field line and strike a detector. If a variety of singly ionized atoms travel at the same speed through the magnetic field, what kind of deflection would you expect? 1. It cannot be predicted. 2. All of them should be deflected by the same amount. 3. The ions with smaller masses will be bent more. correct 4. The ions with smaller masses will be bent less. Explanation: Singly charged ions traveling with the same speed through the same magnetic field will experience the same magnetic force. Their deflections will then depend on their acceler- ations, which in turn depend on their masses. The least massive ions will be deflected the most and the most massive ions will be de- flected the least.