A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar2, where A is a constant and r < R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR5/5∈0r2. (b) Show that the magnitude of the electric field inside (r < R) the sphere is E = Ar3/5∈0. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr.

A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar2, where A is a constant and r < R is measured from the center of the sphere. (a) Show that the magnitude of the electric field outside (r > R) the sphere is E = AR5/5∈0r2. (b) Show that the magnitude of the electric field inside (r < R) the sphere is E = Ar3/5∈0. Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter25: Gauss’s Law

Section: Chapter Questions

Problem 43PQ: The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R),...

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