28.82 A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is J. The current density, although symmetric about the cylinder axis, is not constant and varies according to the relationship 3 = ( ² )e(²-₁ e(r-a)/8 for r ≤ a = 0 for r≥ a where the radius of the cylinder is a = 5.00 cm, r is the radial dis- tance from the cylinder axis, b is a constant equal to 600 A/m, and 8 is a constant equal to 2.50 cm. (a) Let I be the total current passing through the entire cross section of the wire. Obtain an expression for Io in terms of b, 8, and a. Evaluate your expression to obtain a numerical value for Io. (b) Using Ampere's law, derive an expres- sion for the magnetic field B in the region r≥a. Express your answer in terms of Io rather than b. (c) Obtain an expression for the current I contained in a circular cross section of radius r ≤ a and centered at the cylinder axis. Express your answer in terms of lo rather than b. (d) Using Ampere's law, derive an expression for the magnetic field B in the region r ≤ a. (e) Evaluate the magnitude of the magnetic field at r = 8, r = a, and r = 2a.

28.82 A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is J. The current density, although symmetric about the cylinder axis, is not constant and varies according to the relationship 3 = ( ² )e(²-₁ e(r-a)/8 for r ≤ a = 0 for r≥ a where the radius of the cylinder is a = 5.00 cm, r is the radial dis- tance from the cylinder axis, b is a constant equal to 600 A/m, and 8 is a constant equal to 2.50 cm. (a) Let I be the total current passing through the entire cross section of the wire. Obtain an expression for Io in terms of b, 8, and a. Evaluate your expression to obtain a numerical value for Io. (b) Using Ampere's law, derive an expres- sion for the magnetic field B in the region r≥a. Express your answer in terms of Io rather than b. (c) Obtain an expression for the current I contained in a circular cross section of radius r ≤ a and centered at the cylinder axis. Express your answer in terms of lo rather than b. (d) Using Ampere's law, derive an expression for the magnetic field B in the region r ≤ a. (e) Evaluate the magnitude of the magnetic field at r = 8, r = a, and r = 2a.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Ferromagnetism

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Question

28.82 A long, straight, solid cylinder, oriented with its axis in
the z-direction, carries a current whose current density is J. The
current density, although symmetric about the cylinder axis, is not
constant and varies according to the relationship
³ = ( ² ) e (²-a)/³ î€
e(r-a)/8 for r ≤ a
= 0
for r≥ a
where the radius of the cylinder is a = 5.00 cm, r is the radial dis-
tance from the cylinder axis, b is a constant equal to 600 A/m, and
8 is a constant equal to 2.50 cm. (a) Let I be the total current passing
through the entire cross section of the wire. Obtain an expression
for Io in terms of b, 8, and a. Evaluate your expression to obtain a
numerical value for Io. (b) Using Ampere's law, derive an expres-
sion for the magnetic field B in the region r≥ a. Express your
answer in terms of Io rather than b. (c) Obtain an expression for the
current I contained in a circular cross section of radius r ≤ a and
centered at the cylinder axis. Express your answer in terms of lo
rather than b. (d) Using Ampere's law, derive an expression for the
magnetic field B in the region r ≤ a. (e) Evaluate the magnitude of
the magnetic field at r = 8, r = a, and r = 2a.

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