Homework Help: Dielectric Sphere with Free Volume Charge

1. Oct 6, 2011

jegues

1. The problem statement, all variables and given/known data

See figure attached.

2. Relevant equations

3. The attempt at a solution

I'm confused as to how they got their D(r)

Using Gauss' Law,

For r < or = a

$$\oint_{S} \vec{D} \cdot \hat{n} dS = \int_{v} \rho dv$$

$$D(4 \pi r^{2}) = \frac{\rho 4 \pi r^{3}}{3}$$

$$\Rightarrow D = \frac{P_{0}r^{2}}{3a}$$

What am I doing wrong?

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2. Oct 8, 2011

rude man

You have ρ = constant. It's not.