A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.455 T over a region of radius1.70 m.(a) What is the cyclotron frequency?(b) What is the maximum speed acquired by the protons?Part 1 of 4 - ConceptualizeCyclotrons can be used to produce radioactive substances used in diagnosis and treatment. We expect theangular frequency to be on the order of millions of radians per second. We expect the maximum speed of theproton to be a substantial fraction of the speed of light.Part 2 of 4 - CategorizeWe apply the equations of angular frequency to the proton that accelerates in the magnetic field of thecyclotron.Part 3 of 4 - Analyze(a) Cyclotron frequency refers to the angular frequency or angular speed of the accelerated particle. For theangular speed of a proton, we have the following.qB1.60 x 10-19 c0.4550.455 T4.3594.36 x 10' rad/s1.67 x 10-27kgPart 4 of 4 - AnalyzeThe path radius is given bymvR =BqJust before the protons escape, their speed isBqRV =m)1.60 x 10-191.67 x 10¬27kgx 10' m/s.

Given values: magnetic field B = 0.455 T radius r = 1.70 m

A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.455 T over a region of radius 1.70 m. (a) What is the cyclotron frequency? (b) What is the maximum speed acquired by the protons?

A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.455 T over a region of radius 1.70 m. (a) What is the cyclotron frequency? (b) What is the maximum speed acquired by the protons?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

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A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.455 T over a region of radius
1.70 m.
(a) What is the cyclotron frequency?
(b) What is the maximum speed acquired by the protons?
Part 1 of 4 - Conceptualize
Cyclotrons can be used to produce radioactive substances used in diagnosis and treatment. We expect the
angular frequency to be on the order of millions of radians per second. We expect the maximum speed of the
proton to be a substantial fraction of the speed of light.
Part 2 of 4 - Categorize
We apply the equations of angular frequency to the proton that accelerates in the magnetic field of the
cyclotron.
Part 3 of 4 - Analyze
(a) Cyclotron frequency refers to the angular frequency or angular speed of the accelerated particle. For the
angular speed of a proton, we have the following.
qB
1.60 x 10-19 c0.455
0.455 T
4.359
4.36 x 10' rad/s
1.67 x 10
-27
kg
Part 4 of 4 - Analyze
The path radius is given by
mv
R =
Bq
Just before the protons escape, their speed is
BqR
V =
m)
1.60 x 10-19
1.67 x 10¬27
kg
x 10' m/s.

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