Final answer:
The charge configurations within the given regions can be deduced using the divergence of the specified electric flux densities. The result reveals a radial charge density that is proportional to r in the first region, no charge in the second region, and a charge that decreases as 1/r² in the last region.
Step-by-step explanation:
The question pertains to the charge configuration that would produce the specified spherical electric flux densities D1, D2, and D3 in a region having spherical symmetry. By using the divergence operator on each electric flux density, we can infer the charge distribution that causes such fields.
For the region 0 < r < a, we have D1 = rrho0/3 ar. Applying the divergence operator, the result indicates a volume charge density that is directly proportional to the radius, suggesting a uniformly increasing charge density with radial distance within this region.
For the region a < r < b, D2 = 0 suggests there is no charge present in this region as the divergence of zero gives us a zero charge density.
Lastly, for the region r > b, D3 = (a³rho0)/(3r²) ar. Here, the divergence results in a volume charge density that decreases with the square of the distance, implying a charge that is distributed inversely with the square of the radius for this outer region.
The charge configurations can be derived by integrating the divergence of the electric flux density over the volume, which aligns with the interpretation of a Gaussian surface as per Gauss's Law. For instance, the total charge within a spherical volume can be deduced by the electric flux crossing a Gaussian surface.