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electric potential--will rate!!

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Scholar
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Date Posted: 7/24/2008 4:34:10 PM  Status: Live
electric potential--will rate!!
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Question Details:
An insulating solid sphere of radius R has a uniform positive volume charge density and total charge Q.  Find the electric potential at a point inside the sphere that is for r < R.   Take the potential to be zero at infinity.
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Oracle
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Date Posted: 7/24/2008 9:50:15 PM  Status: Live
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Response:
The charge density ρ = Q/(4πR3/3) = 3Q/(4πR3)
use Gauss law to find the electric field E(x) with x < R and x > R
x < R:
E*(4πx2) = (1/εo)*ρ*(4πx3/3)
so E(x) = ρx/(3εo)
x > R
E*(4πx2) = (1/εo)*Q
so E(x) = Q/(4πεox2)
Find the electric potential V(r) for r < R
V(r) =
= ρ(R2 - r2)/(6εo) + Q/(4πεoR)
= Q/(8πεo) * (1/R - r2/R3) + Q/(4πεoR)
= Q * (3R2 - r2)/(8πεoR3)



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