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4. An infinitely long nonconducting solid cylinder of radius a has a nonuniform volume charge density. This density varies with r, the perpendicular distance from its axis, according to p = br², where b is a constant. (a) Show that the linear charge density of the cylinder is given by λ = πba¹/2. Find the expression for the electric field for r

4. An infinitely long nonconducting solid cylinder of radius a has a nonuniform volume charge density. This density varies with r, the perpendicular distance from its axis, according to p = br², where b is a constant. (a) Show that the linear charge density of the cylinder is given by λ = πba¹/2. Find the expression for the electric field for r

College Physics
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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4. An infinitely long nonconducting solid cylinder of radius a has a nonuniform volume charge density. This density varies with r, the perpendicular distance from its axis, according to p = br², where b is a constant. (a) Show that the linear charge density of the cylinder is given by λ = πba¹/2. Find the expression for the electric field for r <a. Hint: Compute for the total charge contained inside a cylinder of length L by considering multiple shells of the cylinder. Afterward, use the relation Q = AL to identify the linear charge density. A cylinder of leviat Consider their for do Come tik circumference of the bylinder segment
Transcribed Image Text:4. An infinitely long nonconducting solid cylinder of radius a has a nonuniform volume charge density. This density varies with r, the perpendicular distance from its axis, according to p = br², where b is a constant. (a) Show that the linear charge density of the cylinder is given by λ = πba¹/2. Find the expression for the electric field for r <a. Hint: Compute for the total charge contained inside a cylinder of length L by considering multiple shells of the cylinder. Afterward, use the relation Q = AL to identify the linear charge density. A cylinder of leviat Consider their for do Come tik circumference of the bylinder segment
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