2. Apply Gauss's law and determine the magnitude of electric field as func-tion of r both inside and outside the sphere. (Inside the sphere, considerregions of two different volume charge densities separately.)3. What fraction of total charge is deposited in both regions of the sphere? You have learned to apply Gauss's law to spherical charged bodies withuniform charge density p. Suppose some tech genius approaches you and askyou to analyse a charged component that his company has developed and willfeature in his next upcoming invention. This charged body that you need tostudy has spherical shape of radius R and it contain positive charge Q. Thetricky part is that its volume charge density is not constant but is function ofdistance from the centre i.e. p(r). This charge density is equal to 3Ar/(2R) forr< R/2 and A[1 – (r/R)²] for R/2 < r < R . The quantity A is a constanthaving units of C/m³.

Gauss law of electrostatics gives us:∮E→.da→=Qencε0………(1)where,Qenc is the charge enclosed in the…

Apply Gauss's law and determine the magnitude of electric field as func- tion of r both inside and outside the sphere. (Inside the sphere, consider regions of two different volume charge densities separately.) What fraction of total charge is deposited in both regions of the sphere?

Apply Gauss's law and determine the magnitude of electric field as func- tion of r both inside and outside the sphere. (Inside the sphere, consider regions of two different volume charge densities separately.) What fraction of total charge is deposited in both regions of the sphere?

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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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

2. Apply Gauss's law and determine the magnitude of electric field as func-
tion 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?

You have learned to apply Gauss's law to spherical charged bodies with
uniform charge density p. 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. p(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.

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