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Medical uses of cyclotrons. The largest cyclotron (see the previous problem) in the United States is the Tevatron at Fermilab, near Chicago, Illinois. It is called a Tevatron be- cause it can accelerate particles to energies in the TeV range (1 tera-eV $=10^{12}$ eV ). Its circumference is $6.4 \mathrm{km},$ and it currently can produce a maximum energy of 2.0 TeV. In a certain medical experiment, protons will be accelerated to energies of 1.25 MeV and aimed at a tumor to destroy its cells. (a) How fast are these protons moving when they hit the tumor? (b) How strong must the magnetic field be to bend the protons in the circle indicated?

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a) $1.55 \times 10^{7} \mathrm{m} / \mathrm{s}$b) $1.58 \times 10^{-4} \mathrm{T}$

Physics 101 Mechanics

Physics 102 Electricity and Magnetism

Chapter 20

Magnetic Field and Magnetic Force

Motion Along a Straight Line

Motion in 2d or 3d

Electric Charge and Electric Field

Gauss's Law

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

Cornell University

University of Washington

University of Winnipeg

McMaster University

Lectures

18:38

In physics, electric flux is a measure of the quantity of electric charge passing through a surface. It is used in the study of electromagnetic radiation. The SI unit of electric flux is the weber (symbol: Wb). The electric flux through a surface is calculated by dividing the electric charge passing through the surface by the area of the surface, and multiplying by the permittivity of free space (the permittivity of vacuum is used in the case of a vacuum). The electric flux through a closed surface is zero, by Gauss's law.

04:28

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H. The term "magnetic field" is often used to refer to the B field. In a vacuum, B and H are the same, whereas in a material medium, B is a component of H. In the latter case, H is the "magnetic field strength", and B is the "magnetic flux".

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Medical uses of cyclotrons…

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Medical Uses of Cyclotrons…

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ssm In the operating room,…

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A cyclotron designed to ac…

so here for part A. We want to find the velocity. We can use the formula for the kinetic energy. This is going to be equal to one house and be squared. And we're getting the kinetic energy so we can simply solve for V and say that this is going to be two times a kinetic energy divided by the mass devoted to the 1/2 power. The mass here is going to be the mass of a proton. So this will be equal to, um, it's actually got a new line. V would be equal to two times 1.25 times 10 to the sixth electron volts times 1.6 times 10 to the negative 19th Jules per electron volts on. Then this would be divided by the mass of a proton 1.67 times 10 to the negative 27th kilograms all again to the 1/2 power this is giving us, um, what's a little bit? Smile 1.55 times 10 to the seven meters per second. And so that would be your answer for party. Um and so we can relate the force this centripetal force to the force of a magnetic field and we come. We can derive the following equation and say that B is equal in q B. Are divided by M and to find the magnetic field. This is simply going to be equal to M v, divided by q R. So at this point, we can say that the were rather we know that the circumference is two pi r and we know that the radius will be simply well to the circumference divided by two pi. So we can rewrite B and so that B is going to be equal to two pi and the divided by q c. Thiss your conference so this would be equal to two pi times the mass 1.67 times 10 to the negative, 27th kilograms and then times 1.55 times 10 to the seventh meters per second, divided by the charge. So this is simply B 1.6 times 10 to the negative 19th cool arms and then times thie circumference. Here, this is going to be a 64 100 meters, and this is going to be equal to 1.59 times 10 to the negative forthe Tesla's again. Ah, this is so low because this is only one proton. If this mass was any greater this this Ah, the magnitude of the magnetic field would would increase. So this is low, mostly because we're dealing with only one proton. And so that would be your answer for part B. That is the end of the solution. Thank you for watching.

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