(a) A solid sphere, made of an insulating material, has a volume charge density of ρ = a/r, where r is the radius from the center of the sphere, a is constant, and a > 0. What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr2dr. (Use the following as necessary: a, r, and ε0.)magnitude E=________direction: radially outward, radially inward, or no direction? (b) What If? What if the charge density as a function of r within the charged solid sphere is given by ρ = a/r2? Find the new magnitude and direction of the electric field within the sphere at radius r. (Use the following as necessary: a, r, and ε0.)magnitude E=_________direction: radially outward, radially inward, or no direction?

Given The volume charge density of the sphere is ρ = a/r. The volume element of the sphere is dV =…

Answered: (a) A solid sphere, made of an…

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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(a) A solid sphere, made of an insulating material, has a volume charge density of ρ = a/r, where r is the radius from the center of the sphere, a is constant, and a > 0. What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4πr²dr. (Use the following as necessary: a, r, and ε₀.)

magnitude E=________

direction: radially outward, radially inward, or no direction?

(b) What If? What if the charge density as a function of r within the charged solid sphere is given by ρ = a/r²? Find the new magnitude and direction of the electric field within the sphere at radius r. (Use the following as necessary: a, r, and ε₀.)

magnitude E=_________

direction: radially outward, radially inward, or no direction?

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