A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗. The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗=2*I0/πa^2 *[1−(r/a)^2]k for r≤a=0 for r≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes.Part A Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≥a.Part B Obtain an expression for the current I contained in a circular cross section of radius r≤a and centered at the cylinder axis.Part C Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≤a.

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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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A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗. The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗=2*I₀/πa^2 *[1−(r/a)^2]k for r≤a=0 for r≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I₀ is a constant having units of amperes.

Part A
Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≥a.

Part B
Obtain an expression for the current I contained in a circular cross section of radius r≤a and centered at the cylinder axis.

Part C
Using Ampere's law, derive an expression for the magnitude of the magnetic field B⃗ in the region r≤a.

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