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A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: p(r) = po (1 – r/R) for r < R p(r) = 0 for r > R where po = 3Q/TR° is a positive constant. (a) Show that the total charge contained in the charge distribution is Q. (b) Show that the electric field in the region r > R is identical to that produced by a point charge Q atr = 0. (c) Obtain an expression for the electric field in the region r < R. (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field. (modified from Young and Freedman, 2014)

A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: p(r) = po (1 – r/R) for r < R p(r) = 0 for r > R where po = 3Q/TR° is a positive constant. (a) Show that the total charge contained in the charge distribution is Q. (b) Show that the electric field in the region r > R is identical to that produced by a point charge Q atr = 0. (c) Obtain an expression for the electric field in the region r < R. (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field. (modified from Young and Freedman, 2014)

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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Subpart D and E

A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: p(r) = po (1 – r/R) for r < R p(r) = 0 for r > R where po = 3Q/TR° is a positive constant. (a) Show that the total charge contained in the charge distribution is Q. (b) Show that the electric field in the region r > Ris identical to that produced by a point charge Q at r = 0. (c) Obtain an expression for the electric field in the region r < R. (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field. (modified from Young and Freedman, 2014)
Transcribed Image Text:A nonuniform, but spherically symmetric, distribution of charge has a charge density p(r) given as follows: p(r) = po (1 – r/R) for r < R p(r) = 0 for r > R where po = 3Q/TR° is a positive constant. (a) Show that the total charge contained in the charge distribution is Q. (b) Show that the electric field in the region r > Ris identical to that produced by a point charge Q at r = 0. (c) Obtain an expression for the electric field in the region r < R. (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field. (modified from Young and Freedman, 2014)
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