An infinitely long hollow cylinder, with radius a and surface charge density σ, spins about the z axis with angular speed w. (a) Using Biot-Savart Law and starting from the magnetic field of a thin slice of the cylinder with thickness dz, calculate the magnetic field at a point on the z-axis by integrating over z. (b) Using a proper path of integration, Use Ampere's law to show that the magnetic field inside the hollow cylinder must be uniform. (c) By choosing a circular path, show that B6 must be zero outside the cylinder (d) Now the angular speed increases so w = at. Using Faraday's Law find the electric field inside and outside the cylinder.
An infinitely long hollow cylinder, with radius a and surface charge density σ, spins about the z axis with angular speed w. (a) Using Biot-Savart Law and starting from the magnetic field of a thin slice of the cylinder with thickness dz, calculate the magnetic field at a point on the z-axis by integrating over z. (b) Using a proper path of integration, Use Ampere's law to show that the magnetic field inside the hollow cylinder must be uniform. (c) By choosing a circular path, show that B6 must be zero outside the cylinder (d) Now the angular speed increases so w = at. Using Faraday's Law find the electric field inside and outside the cylinder.
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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Transcribed Image Text:An infinitely long hollow cylinder, with radius a and surface charge density σ, spins about the z axis
with angular speed w.
(a) Using Biot-Savart Law and starting from the magnetic field of a thin slice of the cylinder with
thickness dz, calculate the magnetic field at a point on the z-axis by integrating over z.
(b) Using a proper path of integration, Use Ampere's law to show that the magnetic field inside
the hollow cylinder must be uniform.
(c) By choosing a circular path, show that B6 must be zero outside the cylinder
(d) Now the angular speed increases so w = at. Using Faraday's Law find the electric field inside
and outside the cylinder.
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