Electric field within a solid sphere

  • Thread starter Gee Wiz
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  • #1
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Homework Statement



A nonconducting, solid sphere of radius a is placed at the center of a spherical conducting shell of inner radius b (> a) and outer radius c, as shown in the figure below. A charge +Q is distributed uniformly through the sphere, which thus carries a charge density ρ (C/m3). The outer shell carries a total charge -3Q.

Find the electric field E(r) within the solid sphere, i.e., at a radius r < a

Homework Equations


∫EdA=Qenclosed/Eo


The Attempt at a Solution



E*4∏r^2=(ρ*(4/3)*∏*a^3)/Eo

I thought I knew what i was doing, but now i'm not quite so sure. I know what i have above is not the correct answer.
 

Answers and Replies

  • #2
BruceW
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Think about how much charge you are enclosing by your Gaussian surface.
 
  • #3
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well, i think that i am enclosing something less than Q. Since Q is uniform over the entire sphere. If i am taking only a portion of that sphere, then i think it should be less.
 
  • #4
BruceW
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yep. well, technically, the charge density is uniform over the entire sphere. You know that a Gaussian sphere of radius a would enclose Q, so how much charge does a Gaussian sphere of radius r(<a) enclose?
 
  • #5
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A ratio of what a enclosed. So like, Qr/a?
 
  • #6
jtbell
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It's a ratio, but not that ratio. Suggestion: first find the charge density ρ in terms of Q and a.
 
  • #7
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That's what i tried to start to do with :E*4∏r^2=(ρ*(4/3)*∏*a^3)/Eo
 
  • #8
jtbell
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You have a sphere of radius a and total charge Q. Forget everything else about the problem for the moment. What is the charge density ρ?

Once you have that, what is the charge on a sphere with the same charge density, but with radius r?
 
  • #9
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charge density p is charge/volume. That's kinda what i was trying to do. Was i just making it more complicated than i needed to. Should i just find p and then multiply it by the new volume that i am trying to find?
 
  • #10
BruceW
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yep. that will give you the charge enclosed by your Gaussian surface (since charge density is constant inside the sphere)
 
  • #11
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ohhh okay. Well thank you all very much
 

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