The document solves for the total charge inside a spherical volume with a uniform charge density p. It uses Gauss's law to determine that the electric field E inside the sphere is equal to p*r/(epsilon_0*3), where r is the radial distance from the center. It then calculates that the total charge inside the sphere is - (4/3) pi * R1^3 * p, where R1 is the radius of the sphere.

1. What is the total charge inside
Solution
a)
as the charge density = p
let the electric field is E
for r < R1
Using Gauss law
p * (4pi/3) * r^3/epsilon_0 = E * 4pi * r^2
solving for E
E = p*r/(epsilon_0*3)
the electric field is p*r/(epsilon_0*3)
b) total charge on the inside surface = - total charge inside
total charge on the inside surface = - (4/3) pi * R1^3 * p
the total charge on the inside surface is - (4/3) pi * R1^3 * p