question in picture and characterize particles,) and mass spectrometers (to identify ions) all rely on this circular motionof charged particles in a magnetic field.At CERN, protons move almost the speed of light in a circle whose radius is over 4 km. In thisproblem we will figure out the magnetic field needed to bend them into this circle. I will walk youthrough the analysis. (The text also goes over a similar example in section 26.3)(a) Draw a diagram of a proton moving in the page, and the B field pointing perpendicular to it (inor out of the page.) Use the right hand rule to decide which way the force points and add theforce vector to your diagram.(b) Write the magnitude of the force in terms of q, v and B.(c) Recall that a force perpendicular to the motion will result in uniform circular motion withcentripetal acceleration ac = v² /r. Use this, the expression for the magnetic force that youalready wrote, and the second law (F=ma) to solve for the magnetic field, in Tesla, that isneeded – if we ignore relativity - to get a radiusr =speed of light) for a proton (mass 1.67 x 10-27 kg and charge 1.6 x 10-19 C.)4 km and speed v equal to c= 3X10$ (the(d) This should look ridiculously small. Why not make the field larger (CERN uses giant multi-Teslamagnets!) and the radius smaller? The answer is relativity. Without getting into the details,the error is that at speeds near c, the effective mass is almost all energy! To account for this,simply replace the kinetic energy we used earlier mv? with the relativistic energy, which isabout 7 TeV (= 71012 eV. ) Convert the energy to SI (J) units, noting that J=(charge e)(energyin eV.)Notice that the expression mv? shows up in our analysis via the net force so you can actuallycontinue to work either in eV or use the converted energy in J. Either way, be careful of units!Revise the analysis to include this correction and recalculate the needed B field. It should nowbe several Tesla, which explains the ever growing size of the CERN accelerator rings. A magnetic field turns the velocity of a particle but does not change the speed, because the force isalways perpendicular to the velocity. Particle accelerators (like CERN,) bubble chambers (to detect

(a) Draw a diagram of a proton moving in the page, and the B field pointing perpendicular to it (in or out of the page.) Use the right hand rule to decide which way the force points and add the force vector to your diagram. (b) Write the magnitude of the force in terms of q, v and B. (c) Recall that a force perpendicular to the motion will result in uniform circular motion with centripetal acceleration ac = v² /r. Use this, the expression for the magnetic force that you already wrote, and the second law (F=ma) to solve for the magnetic field, in Tesla, that is needed – if we ignore relativity - to get a radius r = 4 km and speed v equal to c= 3X10$ (the speed of light) for a proton (mass 1.67 x 10-27 kg and charge 1.6 x 10-19 C.) %3D

(a) Draw a diagram of a proton moving in the page, and the B field pointing perpendicular to it (in or out of the page.) Use the right hand rule to decide which way the force points and add the force vector to your diagram. (b) Write the magnitude of the force in terms of q, v and B. (c) Recall that a force perpendicular to the motion will result in uniform circular motion with centripetal acceleration ac = v² /r. Use this, the expression for the magnetic force that you already wrote, and the second law (F=ma) to solve for the magnetic field, in Tesla, that is needed – if we ignore relativity - to get a radius r = 4 km and speed v equal to c= 3X10$ (the speed of light) for a proton (mass 1.67 x 10-27 kg and charge 1.6 x 10-19 C.) %3D

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter24: Magnetic Fields

Section: Chapter Questions

Problem 79A

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Similar questions

(a) Viewers of Star Trek have heard of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy swore is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then exact them as needed Antimatter annihilates normal matter, producing pure energy. What strength magnetic field is needed to hold antiprotons, moving at 5.0 × l0 m/s in a circular path 2.00 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (b) Is this field strength obtainable with today’s technology or is it a futuristic possibility?
A cyclotron’s oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its ‘dees’ is 60 cm, what is the kinetic energy (in MeV) of the proton beam produced by the accelerator. (e =1.60 × 10-19 C, mp= 1.67 × 10-27 kg, 1 MeV = 1.6 × 10-13 J)
It takes a proton with a kinetic energy of 11 MeV to efficiently change 18O nuclei into 18F. If the magnetic field inside the cyclotron is 1.2 T, what is the radius of the protons’ orbit just before they exit the cyclotron?
In a mass spectrometer, if the following particles were accelerated into an identical magnetic field, which particle will have a lager radius of curvature? You may assume that they enter the mass spectrometer with identical velocity. a) a proton (1p) c) b) a triton (1p+3n) c) a deuteron (1p+1n) d) d) an alpha particle (2p+2n)
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?
Bubble-chamber photographs taken with a 0.40 T magnetic field show at one point a positron moving perpendicular to the field in a 15 cm circle. What is the magnitude of the positron’s momentum at that point?
A proton synchrotron accelerates protons to a kinetic energy of 500 GeV. At this energy, calculate (a) the Lorentz factor, (b) the speed parameter, and (c) the magnetic field for which the proton orbit has a radius of curvature of 750 m.
A positron with kinetic energy 2.00 keV is projected into a uniform magnetic field of magnitude 0.100 T, with its velocity vector making an angle of 89.0° with . Find (a) the period, (b) the pitch p, and (c) the radius r of its helical path.
How strong a magnetic field (B, in Tesla) is needed to keep an electron moving at a speed of (1/100)c in a circular path of radius 1m?
Calculate the cyclotron frequency of an electron in a magnetic field of magnitude 5.20 T in rad/s
CY-1 A cyclotron has an outer radius Rwith a magnetic field B=25.0T. An alternating potential difference of 150,000V exists between the D's. Protons (q=+1.60x10-19C, m=1.673x10-27kg) are injected into the cyclotron near the center with a very low speed. d) By how many eV does the kinetic energy of the proton increase per revolution? e) Find N the number of revolutions needed for B the proton to reach Ekf. f) Use any equation from part a) to find the symbolicexpression for the period T - the time for one revolution of the proton. g) Find the numerical value of T.
A positron with kinetic energy 1.80 keV is projected into a uniform magnetic field of magnitude 0.140 T, with its velocity vector making an angle of 88.0° with the field. Find (a) the period, (b) the pitch p, and (c) the radius r of its helical path.