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Physics for Scientists and Engineers with Modern Physics | 9th Edition | ISBN: 9781133954057 | Authors: Raymond A. Serway John W. Jewett
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An aluminum ring of radius r1 and resistance R is placed

Chapter 31, Problem 12

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QUESTION:

An aluminum ring of radius r1 and resistance R is placed around one end of a long air-core solenoid with n turns per meter and smaller radius r2 as shown in Figure P31.11. Assume the axial component of the field produced by the solenoid over the area of the end of the solenoid is one-half as strong as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of DI/Dt. (a) What is the induced current in the ring? (b) At the center of the ring, what is the magnetic field produced by the induced current in the ring? (c) What is the direction of this field?

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QUESTION:

An aluminum ring of radius r1 and resistance R is placed around one end of a long air-core solenoid with n turns per meter and smaller radius r2 as shown in Figure P31.11. Assume the axial component of the field produced by the solenoid over the area of the end of the solenoid is one-half as strong as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of DI/Dt. (a) What is the induced current in the ring? (b) At the center of the ring, what is the magnetic field produced by the induced current in the ring? (c) What is the direction of this field?

ANSWER:

Step 1 of 4

(a)

The induced emf can be given as,

                                                                   

Here, i is the induced current.

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