Find an electric field around a hollow insulating sphere.

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Homework Statement


An insulating hollow sphere has inner radius a and outer radius b. Within the insulating material the volume charge density is given by ρ(r)=[itex]\alpha[/itex]/r,where [itex]\alpha[/itex] is a positive constant. What is the magnitude of the electric field at a distance r from the center of the shell, where a<r<b?
Express your answer in terms of the variables α, a, r, and electric constant ϵ0.


Homework Equations



E*4[itex]\pi[/itex]r^2 = Q * volume

The Attempt at a Solution



Substituting and integrating with the above formula, I came out with (α/3[itex]\epsilon0[/itex])(r-((a^3)/(r^2)). I cannot tell if the error is with my math, or with the formula I began this process with.
 

Answers and Replies

  • #2
BvU
Science Advisor
Homework Helper
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Hello sport, and welcome to PF.
Apparently you conclude that your answer is in error. How do you know ?
You show your answer, but I can't reconstruct what you do to get there...
Please post some intermediary steps...
 

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