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)

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 22P: Find the electric flux through a rectangular area 3 cm x 2 cm between parallel plates where there is...

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