Thus, B can then be expressed asB=Q/Now we are ready to solve for the charged enclosed by the Gaussian surface.We apply the same definition of volume charge density, to obtain the integral3BdV9enc'o p3/2the difference is now, the limits of r will be from 0 to r. Evaluating the integral and simplifying, we obtainlenc =By substitution to Equation 1 above, then using A =and simplifying, we obtainE = (1/(Qr/R An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is3Bp=p312where B is a constant and r is the distance from the center of the sphere. What is electric field at any point inside the sphere?SolutionTo find the electric field inside the non-uniformly charged sphere, we may apply integration method or the Gauss's Law method.Here, let us use the Gauss's law which is expressed asfE - dÃ= Q/ epsilono%|We will choose a symmetric Gaussian surface, which is the surface of a sphere, then evaluate the dot product to obtainA =(Equation 1)The issue however is how much charge does the Gaussian surface encloses?Since, our sphere is an insulating material, charges will get distributed non-uniformly within the volume of the object. So, we look into the definition of volumecharge density to find the enclosed charge. So, we havedqp=dVBased on the given problem, we can also say thatdqenc3Bp=dV1312Let us first solve for B.Our enclosed charge would have limits from 0 to Q. Then r would have the limits 0 to R. Thus, the equation above becomesR38dVp3/2where dV is the infinitesimal volume.By evaluating the integral and simplifying, we obtain the followingRfor the limits from 0 to R%3D

An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is 3B p= 1312 where B is a constant and r is the distance from the center of the sphere. What is electric field at any point inside the sphere?

An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is 3B p= 1312 where B is a constant and r is the distance from the center of the sphere. What is electric field at any point inside 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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