Particle A has 2 times the mass, 3 times the charge, and 0.9 times the velocity as particle B. They travel in the same direction, and both enter the same constant magnetic field that is perpendicular to their motion. Find the ratio of the cyclotron radius of particle A to that of particle B.
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![**Problem Statement:**
Particle A has 2 times the mass, 3 times the charge, and 0.9 times the velocity as particle B. They travel in the same direction, and both enter the same constant magnetic field that is perpendicular to their motion. Find the ratio of the cyclotron radius of particle A to that of particle B.
**[Answer Box]**: ___](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71da004f-23dc-47ac-9c54-84cf84b3724a%2F67e5009a-d629-43f9-9ecd-096509efbeee%2Fu0ui9ff_processed.png&w=3840&q=75)
The radius of the circular path of a charged particle in a magnetic field is: r = mv/qB.
Magnetic field is given constant.
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- Consider a proton with kinetic energy 10MEV in a cyclotron with magnetic field of 1T. Proton mass is 1.67 1.67 · 10-27 kg . The radius of the orbit is: (a) 0.43 m (b) 0.46 m (c) 0.49 m (d) 0.52 m Correct AnswerHow 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?(a) A beam of highly energetic protons emerges from a cyclotron. Can you assume that there is a magnetic field associated with these particles? Justify your answer. (b) When a current travels through the coils of a coil spring, the coil contracts as if it were compressed. What is your explanation for the fact?
- At the Fermilab accelerator in Weston, Illinois, singly charged ions with momentum 3.3 × 10−16 kg m/s are held in a circular orbit of radius 1.00 km by an upward magnetic field. What B field must be used to maintain the ions in this orbit? (qion = 1.60 × 10−19 C)An electron moves in an uniform magnetic field (with the orbital plane perpendicular to the field). If the cylotron radius of the electron is 60 cm and it's kinetic energy is 9.6 keV, find the electron's speed, the magnitude of the magnetic field, the cyclotron frequency, and the period of the motion. Use me=9.11×10−31me=9.11×10-31 kg, e=1.6×10−19e=1.6×10-19 C, and 1 T = 104 G. The speed, v = Units Correct . The magnetic field, B = Units . The cyclotron frequency, f = Units Correct . The period, T = Units Correct .6.13 Alpha particles are accelerated in a superconducting cyclotron operating with a magnetic field of 4 T. If the energy of extracted a particles is 12.5 MeV, calculate the value of the extraction radius in cm. 6.14 Calculate the cyclotron frequency in Problem 6.13.
- For synchronous particles to remain on a constant radius in a synchrotron, show that the time derivative of the magnetic field is given by dB BATtum dt 2xqpR where ATturn is the kinetic energy gain per turn, R is the radius and p the bending radius, q the charge of a particle, ẞ=v/c. Assume the particles are accelerated on crest in a synchrotron of 10 GeV (kinetic energy) where the magnetic field reaches 1.5 Tesla in one second, following a linear variation. Calculate the bending radius and assuming R~1.5p, evaluate the accelerating voltage in kV.A particle in the cyclotron shown in Figure 28.16a gains energy qAV from the alternating power supply each time it passes from one dee to the other. The time interval for each full 2qAV g*BAV 2nm orbit is T = 21 so the particle's average rate of increase in energy is qB 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 dr 1 Δν particle's path is given by dt r nBPlease answer questions d and e only. Thanks!