An infinite cylinder of radius R has a charge density given by p(r) = ar", 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 has magnitude ar6 E(r) = 7€0 Which direction does it point in?

An infinite cylinder of radius R has a charge density given by p(r) = ar", 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 has magnitude ar6 E(r) = 7€0 Which direction does it point in?

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 43P: A very long, thin wile has a uniform linear charge density of 50C/m . What is the electric field at...

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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 has magnitude
ar6
E(r)
7€0
Which direction does it point in?

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