An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aR E(r) = 7€or is the same as that obtained if all the charge is concentrated in an infinitely thin wire.

An infinite cylinder of radius R has a charge density given by p(r) = ar³, where r is the perpendicular distance from the axis of the cylinder, and a is a constant. Show that the electric field for r > R given by aR E(r) = 7€or is the same as that obtained if all the charge is concentrated in an infinitely thin wire.

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

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

An infinite cylinder of radius R has a charge density given by
p(r) = ar³,
where r is the perpendicular distance from the axis of the cylinder, and a is a constant.
Show that the electric field for r > R given by
aRT
E(r) :
7€or
is the same as that obtained if all the charge is concentrated in an infinitely thin wire.

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