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Physics / Physics for Scientists and Engineers with Modern Physics 9 / Chapter 31 / Problem 82

Physics for Scientists and Engineers with Modern Physics | 9th Edition | ISBN: 9781133954057 | Authors: Raymond A. Serway John W. Jewett

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A betatron is a device that accelerates electrons to

Chapter 31, Problem 82

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QUESTION:

A betatron is a device that accelerates electrons to energies in the MeV range by means of electromagnetic induction. Electrons in a vacuum chamber are held in a circular orbit by a magnetic field perpendicular to the orbital plane. The magnetic field is gradually increased to induce an electric field around the orbit. (a) Show that the electric field is in the correct direction to make the electrons speed up. (b) Assume the radius of the orbit remains constant. Show that the average magnetic field over the area enclosed by the orbit must be twice as large as the magnetic field at the circles circumference.

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QUESTION:

A betatron is a device that accelerates electrons to energies in the MeV range by means of electromagnetic induction. Electrons in a vacuum chamber are held in a circular orbit by a magnetic field perpendicular to the orbital plane. The magnetic field is gradually increased to induce an electric field around the orbit. (a) Show that the electric field is in the correct direction to make the electrons speed up. (b) Assume the radius of the orbit remains constant. Show that the average magnetic field over the area enclosed by the orbit must be twice as large as the magnetic field at the circles circumference.

ANSWER:

Step 1 of 5

(a)

The force on the charge can be given as,

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