Final answer:
To determine the electric fields in different regions around a hollow spherical shell with a negative point charge at the center and positive charge distributed through its volume, Gauss's Law is used. The electric field is zero inside the hollow part, while it is calculated based on enclosed charge within the shell and acts as a point charge effect outside the shell.
Step-by-step explanation:
The question addresses the concept of electric fields within and around a hollow insulating spherical shell that has a negative point charge at its center and a positive charge distributed within its volume. Gauss's Law, which relates the electric field to the charge distribution within a closed surface, can be used to determine the electric field in different regions.
(a) For r < R1, since the point is inside the hollow part of the spherical shell where there is no charge, the electric field will be zero based on Gauss's Law.
(b) For R1 < r < R2, the electric field can be calculated by considering a Gaussian surface just inside the shell and using Gauss's Law to relate the electric field to the amount of charge enclosed. Since the charge is uniformly distributed, the electric field at r can be found using the formula for the charge inside the Gaussian surface divided by the permittivity of free space and surface area.
(c) For r > R2, the electric field would be as if all the charge within the sphere was concentrated at the center, by adding algebraically the charge -Q at the center and the +7Q distributed in the volume. Again, Gauss's Law can be applied to find the electric field, treating the charges as if they were a point charge.