Charge density as a function of r

AI Thread Summary
The discussion focuses on finding the volume charge density (ρr) as a function of distance (r) for a sphere with a specified electric field (Er=ER(r^4/R^4)). Participants reference Gauss's law and the relationship between charge density and electric field. There is confusion regarding the calculation of charge (dQ) and its relation to volume, as the volume of a sphere is not accurately represented by 4πr^2. The correct approach involves using the divergence of the electric field to relate it to charge density. Clarification on these concepts is necessary to solve for ρ effectively.
JJfortherear
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Homework Statement



Sphere of radius R, Er=ER(r4/R4)
Find the volume charge density (ρr) as a function of r

Homework Equations



Gauss's law

The Attempt at a Solution



I get that dQ=4πr2ρrdr, but have no idea how to solve for ρ
 
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Have you seen the following form of Gauss's Law?

\nabla\cdot E = \rho/\epsilon_0
 
like kuruman said, its application of gauss's law

Flux = \ointE (dot) dA = q/e

you found q to be 4πr2ρ, but p = Charge / Volume

but 4πr^2 isn't the volume of a sphere
 

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