A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. a. The charge within a small volume dV is dq=ρdV. The integral of ρdV over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R.Hint: Let dV be a spherical shell of radius r and thickness dr. What is the volume of such a shell? Express your answer in terms of the variables Q and R. b. Use Gauss's law to find an expression for the magnitude of the electric field strength E inside the sphere, r≤R, in terms of Q and R. Express your answer in terms of the variables R, r, Q, and ϵ0.

A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. a. The charge within a small volume dV is dq=ρdV. The integral of ρdV over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R.Hint: Let dV be a spherical shell of radius r and thickness dr. What is the volume of such a shell? Express your answer in terms of the variables Q and R. b. Use Gauss's law to find an expression for the magnitude of the electric field strength E inside the sphere, r≤R, in terms of Q and R. Express your answer in terms of the variables R, r, Q, and ϵ0.

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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