Problem 6.12 An infinitely long cylinder, of radius R, carries a “frozen-in” magne- tization, parallel to the axis, M = ks z, where k is a constant and s is the distance from the axis; there is no free current anywhere. Find the magnetic field inside and outside the cylinder by two different methods: (a) As in Sect. 6.2, locate all the bound currents, and calculate the field they produce. (b) Use Ampère's law (in the form of Eq. 6.20) to find H, and then get B from Eq. 6.18. (Notice that the second method is much faster, and avoids reference to the bound currents.) any explicit

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 6.12 An infinitely long cylinder, of radius R, carries a “frozen-in” magne-
tization, parallel to the axis,
M = ks z,
where k is a constant and s is the distance from the axis; there is no free current
anywhere. Find the magnetic field inside and outside the cylinder by two different
methods:
(a) As in Sect. 6.2, locate all the bound currents, and calculate the field they
produce.
(b) Use Ampère's law (in the form of Eq. 6.20) to find H, and then get B from
Eq. 6.18. (Notice that the second method is much faster, and avoids
reference to the bound currents.)
any explicit
Transcribed Image Text:Problem 6.12 An infinitely long cylinder, of radius R, carries a “frozen-in” magne- tization, parallel to the axis, M = ks z, where k is a constant and s is the distance from the axis; there is no free current anywhere. Find the magnetic field inside and outside the cylinder by two different methods: (a) As in Sect. 6.2, locate all the bound currents, and calculate the field they produce. (b) Use Ampère's law (in the form of Eq. 6.20) to find H, and then get B from Eq. 6.18. (Notice that the second method is much faster, and avoids reference to the bound currents.) any explicit
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