A magnetic fi eld of 1.4 T is used to accelerate 10.0- MeV protons in a cyclotron. (a) What is the radius of the magnet? (b) What is the cyclotron frequency?
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A magnetic fi eld of 1.4 T is used to accelerate 10.0- MeV protons in a cyclotron. (a) What is the radius of the magnet? (b) What is the cyclotron frequency?
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- As a charged particle is shot to a magnetic field B with a speed v perpendicular to B, the particle's motion gets modified and the so called "cyclotron radius" relates to its charge directly inversely O as va3. What magnetic field is required for the 7.0-TeV protons in the 4.25-km radius Large Hadron Collider (LHC)? 4. Show that the energy of a particle (charge q.) in a synchotron, in the relativistic limit (v z c), is given by E = Brc, where E is measured in eV, B is the magnetic field, and r is the radius of the orbit.(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?
- In nuclear power plants, atoms are split apart to form smaller atoms releasing energy 20 in a process called nuclear fission. Calculate the electrical power that is released in one hour due to splitting 200 g of Uranium-235, taking the disintegration energy per event to be 208 MeV.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.Beams of p- mesons are used in radiation therapy for certain cancers. The energy comes from the complete decay of the p- to stable particles. (a) Write out the complete decay of a p- meson to stable particles. What are these particles? (b) How much energy is released from the complete decay of a single p- meson to stable particles? (You can ignore the very small masses of the neutrinos.) (c) How many p- mesons need to decay to give a dose of 50.0 Gy to 10.0 g of tissue? (d) What would be the equivalent dose in part (c) in Sv and in rem? Consult Table 43.3 and use the largest appropriate RBE for the particles involved in this decay.
- 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.To measure the muon magnetic moment a 2.9-T uniform magnetic field is used. How much energy is stored in the field if the experimental chamber where the field is created has dimensions of 65 cm×35 cm×60 cm? The energy, ? How long will it take to “switch on” the field if the experiment uses a 1.5-kW power supply? Time ?Please answer questions d and e only. Thanks!