Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius r2 with a volume density given by p= Por1/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?

Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius r2 with a volume density given by p= Por1/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?

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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Question

Charge is distributed throughout a spherical shell of inner radius ₁ and outer radius r2 with a volume
density given by p= Por1/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
Qencl
(Answer in terms of given quantities, po, r1, 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<r2. For a spherical surface of radius r between ₁ and
T2, 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 ₁ and r2? Finish the application of
Gauss's Law to find the elcetric field as a function of distance.
E(r)
e. What is the electric field for distances less than r₁?
E(r< r₁) =
=
for r1 <r<r₂.
7

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