76 Bainbridge's mass spectrometer,shown in Fig. 28-54, separates ionshaving the same velocity. The ions, af-ter entering through slits, S, and S2,pass through a velocity selector com-posed of an electric field produced bythe charged plates P and P', and amagnetic field B perpendicular to theelectric field and the ion path. Theions that then pass undeviatedthrough the crossed E and B fields Figure 28-54 Problem 76.enter into a region where a secondmagnetic field B' exists, where they are made to follow circularpaths. A photographic plate (or a modern detector) registers theirarrival. Show that, for the ions, qlm = E/rBB', where r is the radiusof the circular orbit.S,PlateP IPB'

Answered: Image /qna-images/answer/d0055d3c-c13c-4e67-bac0-5438d741b163.jpg

Answered: 76 Bainbridge's mass spectrometer,…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter30: Atomic Physics

Section: Chapter Questions

Problem 67PE: Integrated Concepts Prove that the velocity of charged particles moving along a straight path...

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Integrated Concepts Prove that the velocity of charged particles moving along a straight path through perpendicular electric and magnetic fields is v=E/B. Thus crossed electric and magnetic fields can be used as a velocity selector independent of the charge and mass of the particle involved.
A patient in an MRI unit turns his head quickly to one side and experiences momentary dizziness and a strange taste in his mouth. Discuss the possible causes.
A particle in the cyclotron shown in Figure 28.16a gains energy qV from the alternating power supply each time it passes from one dee to the other. The time interval for each full orbit is T=2=2mqB so the particles average rate of increase in energy is 2qVT=q2BVm Notice that this power input is constant in time. On the other hand, the rate of increase in the radius r of its path is not constant. (a) Show that the rate of increase in the radius r of the panicles path is given by drdt=1rVB (b) Describe how the path of the particles in Figure 28.16a is consistent with the result of part (a). (c) At what rate is the radial position of the protons in a cyclotron increasing immediately before the protons leave the cyclotron? Assume the cyclotron has an outer radius of 0.350 m, an accelerating voltage of V = 600 V, and a magnetic field of magnitude 0.800 T. (d) By how much does the radius of the protons path increase during their last full revolution? Figure 28.16 (a) A cyclotron consists of an ion source at P, two does D1 and D2 across which an alternating potential difference is applied, and a uniform magnetic field. (The south pole of the magnet is not shown.) (b) The first cyclotron, invented by E. O. Lawrence and M. S. Livingston in 1934.
Integrated Concepts If electric and magnetic field strengths vary sinusoidally in time, being zero at t = 0, then E = E0 sin 2ft and B = B0 sin 2 ft. Let f = 1.00 GHz here. (a) When are the field strengths first zero? (b) When do they reach their most negative value? (c) How much time is needed for them to complete one cycle?
A conducting sheet lies in a plane perpendicular to a magnetic field B that is below the sheet. If B oscillates at a high frequency and the conductor is made of a material of low resistivity, the region above the sheet is effectively shielded from B . Explain why. Will the conductor shield this region from static magnetic fields?
Can an antenna be any length? Explain your answer.
Integrated Concepts A very large, superconducting solenoid such as one used in MRI scene, stores 1.00 MJ of energy in its magnetic field when 100 A flows. (a) Find its serf-inductance. (b) If the coils “go normal,” they gain resistance and start to dissipate thermal energy. What temperature increase is produced it all the stored energy goes into heating the 1000 kg magnet, given its average speci?c heat is 200 J/kg(°C?
Lunar astronauts placed a reflector on the Moon's Surface, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. (a) To what accuracy in meters can the distance to the Moon be determined, if this time can be measured to 0.100 ns? (b) What percent accuracy is this, given the average distance to the Moon is 3.84108m ?
A mass spectrometer is being used to separate common oxygen- 16 from the much rarer oxygen-18, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice s deposited.) The ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is 2.661026kg, , and they are singly charged and travel at 5.00106m/s in a 1.20-T magnetic field. What is the separation between their path when they hit a target after travet5ing a semicircle?
A velocity selector in a mass spectrometer uses a 0.100-T magnetic field, (a) What electric field strength is needed to select a speed of 4.0106m/s fb) What is the voltage between the plates if they are separated by 1.00 cm?
Unreasonable results To construct a non-mechanical water meter, a 0.500-T magnetic field is placed across the supply water pipe to a home and the Hall voltage is recorded, (a) Find the flow rate through a 3.00-cm-diameter pipe if the Hall voltage is 60.0 mV. (b) What would the Hail voltage be for the same flow rate through a 10,0-cm- diameter pipe with tire same field applied?
Check Your Understanding Could a purely electric field propagate as a wave through a vacuum without a magnetic field? Justify your answer.

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