An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is p = 3B / r3/2 (division) where is a constant and r is the distance from the center of the sphere. What is electric field at any point inside the sphere?Continuation of the problem can be seen in the images. Thanks! where dV is the infinitesimal volume.By evaluating the integral and simplifying, we obtain the followingQ=Rfor the limits from 0 to RThus, B can then be expressed asB =QINow 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 integral3B„3/2lenc =Ap-the difference is now, the limits of r will be from 0 to r. Evaluating the integral and simplifying, we obtaindenc =By substitution to Equation 1 above, then using A =,and simplifying, we obtainE = (1/XQr/R SolutionTo find the electric field inside the non-uniformly charged sphere, we may apply integration method or the Gauss's Lawmethod.Here, let us use the Gauss's law which is expressed asfĒ - dÃ =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, welook into the definition of volume charge density to find the enclosed charge. So, we havedqdVBased on the given problem, we can also say thatdqencp=3BdVp312Let 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 becomes.R3BdVp3/2Q =

The volume charge density is given y the charge per unit volume. According to the gauss's theorem,…

An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is p = 3B / r3/2 (division) where is a constant and r is the distance from the center of the sphere. What is electric field at any point inside the sphere? Continuation of the problem can be seen in the images. Thanks!

An insulating sphere with radius R contains a total non-uniform charge (i.e. Hydrogen atom) Q such that its volume charge density is p = 3B / r3/2 (division) where is a constant and r is the distance from the center of the sphere. What is electric field at any point inside the sphere? Continuation of the problem can be seen in the images. Thanks!

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 86AP: Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2...

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