Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 28, Problem 37AP
To determine
The difference in cyclotron frequencies of the two ions.
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The magnetic poles of a small cyclotron produce a magnetic field with magnitude 0.85 T. The poles have a radius of 0.40 m, which is the maximum radius of the orbits of the accelerated particles. (a) What is the maximum energy to which protons (q = 1.60 * 10-19 C, m = 1.67 * 10-27 kg) can be accelerated by this cyclotron? Give your answer in electron volts and in joules. (b) What is the time for one revolution of a proton orbiting at this maximum radius? (c) What would the magnetic-field magnitude have to be for the maximum energy to which a proton can be accelerated to be twice that calculated in part (a)? (d) For B = 0.85 T, what is the maximum energy to which alpha particles (q = 3.20 * 10-19 C, m = 6.64 * 10-27 kg) can be accelerated by this cyclotron? How does this compare to the maximum energy for protons?
The mass of an ion can be determined by measuring its cyclotron frequency in a strong magnetic field. The cyclotron frequency of ion X+ (with charge q=1.6×10−19Cq=1.6×10-19C is measured to be 2.3 MHz in a 1.8 T magnetic field. What is the mass of ion X+ in atomic mass units? Note: one atomic mass unit is 1 amu = 1.66×10-27 kg.)
What is the radius of a proton's trajectory when it moves at 2.4x106 m/s perpendicular to a magnetic field whose strength is 0.08 T? Mass of the proton is 1.67x10-27 kg and the charge is +1.6x10-19 C.
Chapter 28 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 28.1 - An electron moves in the plane of this paper...Ch. 28.2 - Prob. 28.2QQCh. 28.4 - A wire carries current in the plane of this paper...Ch. 28.5 - (i) Rank the magnitudes of the torques acting on...Ch. 28 - At the equator, near the surface of the Earth, the...Ch. 28 - Consider an electron near the Earths equator. In...Ch. 28 - Find the direction of the magnetic field acting on...Ch. 28 - A proton moving at 4.00 106 m/s through a...Ch. 28 - A proton travels with a speed of 5.02 106 m/s in...Ch. 28 - Prob. 6P
Ch. 28 - Prob. 7PCh. 28 - An accelerating voltage of 2.50103 V is applied to...Ch. 28 - A proton (charge + e, mass mp), a deuteron (charge...Ch. 28 - Prob. 10PCh. 28 - Review. One electron collides elastically with a...Ch. 28 - Review. One electron collides elastically with a...Ch. 28 - Review. An electron moves in a circular path...Ch. 28 - A cyclotron designed to accelerate protons has a...Ch. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - A cyclotron (Fig. 28.16) designed to accelerate...Ch. 28 - A particle in the cyclotron shown in Figure 28.16a...Ch. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - A wire carries a steady current of 2.40 A. A...Ch. 28 - Prob. 22PCh. 28 - Review. A rod of mass 0.720 kg and radius 6.00 cm...Ch. 28 - Review. A rod of mass m and radius R rests on two...Ch. 28 - Prob. 25PCh. 28 - Consider the system pictured in Figure P28.26. A...Ch. 28 - A strong magnet is placed under a horizontal...Ch. 28 - In Figure P28.28, the cube is 40.0 cm on each...Ch. 28 - Prob. 29PCh. 28 - A 50.0-turn circular coil of radius 5.00 cm can be...Ch. 28 - You are in charge of planning a physics magic show...Ch. 28 - Prob. 32PCh. 28 - A rectangular coil consists of N = 100 closely...Ch. 28 - A rectangular loop of wire has dimensions 0.500 m...Ch. 28 - Prob. 35PCh. 28 - A Hall-effect probe operates with a 120-mA...Ch. 28 - Prob. 37APCh. 28 - Prob. 38APCh. 28 - Prob. 39APCh. 28 - Prob. 40APCh. 28 - Prob. 41APCh. 28 - Prob. 42APCh. 28 - A proton having an initial velocity of 20.0iMm/s...Ch. 28 - Prob. 44APCh. 28 - Prob. 45APCh. 28 - Why is the following situation impossible? Figure...Ch. 28 - A heart surgeon monitors the flow rate of blood...Ch. 28 - Prob. 48APCh. 28 - Prob. 49CPCh. 28 - Protons having a kinetic energy of 5.00 MeV (1 eV...Ch. 28 - Review. A wire having a linear mass density of...
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- The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons is 0.40 m. (a) What is the kinetic energy of the protons when they are ejected from the cyclotron? (b) What Is this energy in MeV? (c) Through what potential difference would a proton have to be accelerated to acquire this kinetic energy? (d) What is the period of tire voltage source used to accelerate the piotons? (e) Repeat tire calculations for alpha-particles.arrow_forwardA proton precesses with a frequency p in the presence of a magnetic field. If the intensity of the magnetic field is doubled, what happens to the precessional frequency?arrow_forwardA spacecraft is in 4 circular orbit of radius equal to 3.0 104 km around a 2.0 1030 kg pulsar. The magnetic field of the pulsar at that radial distance is 1.0 102 T directed perpendicular to the velocity of the spacecraft. The spacecraft is 0.20 km long with a radius of 0.040 km and moves counter-clockwise in the xy-plane around the pulsar. (a) What is the speed of the spacecraft? (b) If the magnetic field points in the positive z-direction, is the emf induced from the back to the front of the spacecraft or from side to side? (c) Compute the induced emf. (d) Describe the hazards for astronauts inside any spacecraft moving in the vicinity of a pulsar.arrow_forward
- (a) An oxygen16 ion with a mass at 2.661026kg travels at 5.00106m/s perpendicular to a 1.20T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the radio of this charge to the charge of an electron? (c) Discuss why the radio found in (b) should be an integer.arrow_forwardAn alpha-particle ( m=6.641027kg , q=3.21019C ) travels in a circular path of radius 25 cm in a uniform magnetic field of magnitude 1.5 T. (a) What is the speed of the particle? (b) What is the kinetic energy in electron-volts? (c) Through what potential difference must the particle be accelerated in order to give it this kinetic energy?arrow_forwardA mass spectrometer (Fig. 30.40, page 956) operates with a uniform magnetic field of 20.0 mT and an electric field of 4.00 103 V/m in the velocity selector. What is the radius of the semicircular path of a doubly ionized alpha particle (ma = 6.64 1027 kg)?arrow_forward
- An electron in a TV CRT moves with a speed of 6.0107 m/s, in a direction perpendicular to Earth's field, which has a strength of 5.0105 T. (a) What strength electric field must be applied perpendicular to the Earth’s field to make the election moves in a straight line? (b) If this is done between plates separated by 1.00 cm, what is the voltage applied? (Note that TVs are usually surrounded by a ferromagnetic material to shield against external magnetic fields and avoid the need for such a collection,)arrow_forwardWhat magnetic field is required in order to confine a proton moving with a speed of 4.0 × 106 m/s to a circular orbit of radius 10 cm?arrow_forwardDetermine the initial direction of the deflection of charged particles as they enter the magnetic fields as shown in Figure P22.2. Figure P22.2.arrow_forward
- The strengths of the fields in the velocity selector of a Bainbridge mass spectrometer are B = 0.500 T and E=1.2105 Van, and tire strength of the magnetic field that separates the ions is Bo=0.750 T. A stream of singly charged Li ions is found to bend in a circular arc of radius 2.32 cm. What is the mass of the Li ions?arrow_forwardAn electron of kinetic energy 2000 eV passes between parallel plates that are 1.0 an apart and kept at a potential difference of 300 V. What is the strength of the uniform magnetic field B that will allow the electron to travel undeflected through the plates? Assume E and B are perpendicular.arrow_forwardA negative charge, q = -7.2 nC follows a circular path due to the force caused by the magnetic field. If the magnetic field, B = 4.1 T causes charge to follow a radius of r = 3.2 µm, how fast (v = ?), in m/s, does the charge move? The mass of the charge is 5.56 x 10^-22 kg. Disregard any effects caused by special relativity.arrow_forward
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