Suppose that the current density carried by an infinite cylindrical wire is not uniform but in fact varies as Jz(u) = J0 * [1 - (u2 / R2)], where J0 is the value of the current density at the wire's center, R is the radius of the wire, and u is distance from the axis of the wire. Assuming that the magnetic field is circular, compute the wire's magnetic field both inside and outside the wire. (Ampere's law makes even nonuniform current densities manageable.) (Hint: The answer is BФ = 0.25 * μ0 * J0 * R on surface at u = R.)

Suppose that the current density carried by an infinite cylindrical wire is not uniform but in fact varies as Jz(u) = J0 * [1 - (u2 / R2)], where J0 is the value of the current density at the wire's center, R is the radius of the wire, and u is distance from the axis of the wire. Assuming that the magnetic field is circular, compute the wire's magnetic field both inside and outside the wire. (Ampere's law makes even nonuniform current densities manageable.) (Hint: The answer is BФ = 0.25 * μ0 * J0 * R on surface at u = R.)

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter12: Sources Of Magnetic Fields

Section: Chapter Questions

Problem 85AP: , A ray long, thick, cylindrical wire of radius R carries a current density J that varies across its...

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