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Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius 12 with a volume density given by p= POT1/T, where Po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r > r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Because the charge density is a function of r, rather than being able to multiply the charge density by the volume, now you need to integrate over the volume. The amount of charge in a spherical shell of radius r and thickness dr is p(r) - 4r dr; integrate this from r = r₁ to r = r₂ to obtain the total amount of charge. Qencl (Answer in terms of given quantities, Po, 71, 72, and physical constants ke and/or eo. Use underscore () for subscripts, and spell out Greek letters.) b. What is the electric field as a function of r for distances greater than r2? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r>r2) = c. Now let's work on the "mantle" layer, r₁

Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius 12 with a volume density given by p= POT1/T, where Po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r > r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Because the charge density is a function of r, rather than being able to multiply the charge density by the volume, now you need to integrate over the volume. The amount of charge in a spherical shell of radius r and thickness dr is p(r) - 4r dr; integrate this from r = r₁ to r = r₂ to obtain the total amount of charge. Qencl (Answer in terms of given quantities, Po, 71, 72, and physical constants ke and/or eo. Use underscore () for subscripts, and spell out Greek letters.) b. What is the electric field as a function of r for distances greater than r2? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r>r2) = c. Now let's work on the "mantle" layer, r₁

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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Charge is distributed throughout a spherical shell of inner radius r₁ and outer radius r2 with a volume density given by p= Pori/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r > r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Because the charge density is a function of r, rather than being able to multiply the charge density by the volume, row you need to integrate over the volume. The amount of charge in a spherical shell of radius r and thickness dr is p(r). 4tr²dr; integrate this from r = r₁ to r = r₂ to obtain the total amount of charge. Qencl= (Answer in terms of given quantities, po, 71, 72, and physical constants ke and/or Eo. Use underscore ("") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of r for distances greater than r2? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r>r2)= c. Now let's work on the "mantle" layer, r₁ <r < 72. For a spherical surface of radius r between r₁ and T2₂, how much charge is enclosed inside this Gaussian surface? Hint for finding charge within r Qencl(r) = (Answer in terms of given quantities and the variable r.) d. What is the electric field as a function of r for distances between r₁ and r2? Finish the application of Gauss's Law to find the elcetric field as a function of distance. E(r) for ri<r<1₂. e. What is the electric field for distances less than r₁? E(r<r₁)= Submit Question C Search or type URL &
Transcribed Image Text:Charge is distributed throughout a spherical shell of inner radius r₁ and outer radius r2 with a volume density given by p= Pori/r, where po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius r > r2, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Because the charge density is a function of r, rather than being able to multiply the charge density by the volume, row you need to integrate over the volume. The amount of charge in a spherical shell of radius r and thickness dr is p(r). 4tr²dr; integrate this from r = r₁ to r = r₂ to obtain the total amount of charge. Qencl= (Answer in terms of given quantities, po, 71, 72, and physical constants ke and/or Eo. Use underscore ("") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of r for distances greater than r2? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r>r2)= c. Now let's work on the "mantle" layer, r₁ <r < 72. For a spherical surface of radius r between r₁ and T2₂, how much charge is enclosed inside this Gaussian surface? Hint for finding charge within r Qencl(r) = (Answer in terms of given quantities and the variable r.) d. What is the electric field as a function of r for distances between r₁ and r2? Finish the application of Gauss's Law to find the elcetric field as a function of distance. E(r) for ri<r<1₂. e. What is the electric field for distances less than r₁? E(r<r₁)= Submit Question C Search or type URL &
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