You have learned to apply Gauss’s law to spherical charged bodies with uniform charge density ρ. Suppose some tech genius approaches you and ask you to analyse a charged component that his company has developed and will feature in his next upcoming invention. This charged body that you need to study has spherical shape of radius R and it contain positive charge Q. The tricky part is that its volume charge density is not constant but is function of distance from the centre i.e. ρ(r). This charge density is equal to 3Ar/(2R) for r ≤ R/2 and A[1 − (r/R) 2 ] for R/2 ≤ r ≤ R . The quantity A is a constant having units of C/m3 . 1. How would this constant A be expressed in terms of total charge Q and radius R of the sphere? 2. Apply Gauss’s law and determine the magnitude of electric field as function of r both inside and outside the sphere. (Inside the sphere, consider regions of two different volume charge densities separately.) 3. What fraction of total charge is deposited in both regions of the sphere? 4. What is the magnitude of of electric field at point at point R/2?
You have learned to apply Gauss’s law to spherical charged bodies with uniform charge density ρ. Suppose some tech genius approaches you and ask you to analyse a charged component that his company has developed and will feature in his next upcoming invention. This charged body that you need to study has spherical shape of radius R and it contain positive charge Q. The tricky part is that its volume charge density is not constant but is function of distance from the centre i.e. ρ(r). This charge density is equal to 3Ar/(2R) for r ≤ R/2 and A[1 − (r/R) 2 ] for R/2 ≤ r ≤ R . The quantity A is a constant having units of C/m3 . 1. How would this constant A be expressed in terms of total charge Q and radius R of the sphere? 2. Apply Gauss’s law and determine the magnitude of electric field as function of r both inside and outside the sphere. (Inside the sphere, consider regions of two different volume charge densities separately.) 3. What fraction of total charge is deposited in both regions of the sphere? 4. What is the magnitude of of electric field at point at point R/2?
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
You have learned to apply Gauss’s law to spherical charged bodies with
uniform charge density ρ. Suppose some tech genius approaches you and ask
you to analyse a charged component that his company has developed and will
feature in his next upcoming invention. This charged body that you need to
study has spherical shape of radius R and it contain positive charge Q. The
tricky part is that its volume charge density is not constant but is function of
distance from the centre i.e. ρ(r). This charge density is equal to 3Ar/(2R) for
r ≤ R/2 and A[1 − (r/R)
2
] for R/2 ≤ r ≤ R . The quantity A is a constant
having units of C/m3
.
1. How would this constant A be expressed in terms of total charge Q and
radius R of the sphere?
2. Apply Gauss’s law and determine the magnitude of electric field as function of r both inside and outside the sphere. (Inside the sphere, consider
regions of two different volume charge densities separately.)
3. What fraction of total charge is deposited in both regions of the sphere?
4. What is the magnitude of of electric field at point at point R/2?
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