Final answer:
Without the complete and correct volume charge density expression, we cannot precisely calculate the maximum value of p, the total charge in the first octant, or the value of b. The student is encouraged to provide the correct charge density expression for a detailed solution.
Step-by-step explanation:
To address the question regarding the maximum value of density, we evaluate the expression provided for p within the given limits, and we can infer that the maximum value occurs when all variables are at their maximum within the given ranges. Unfortunately, the charge density function provided in the question seems to have a typo or is incomplete, making it impossible to provide a precise answer without the correct expression for p.
For part (b), computing the total charge in the first octant involves integrating the charge density over the volume defined by 0 ≤ x, y, z ≤ 0.01 m. Unfortunately, the precise method of integration depends on the correct expression for the volume charge density, which is not fully provided.
Regarding part (c), the aim is to find the value of b such that the total charge within a sub-volume defined by 0 ≤ ρ ≤ β, 0 ≤ Θ ≤ ψ/2, and z ≥ 0 is exactly half of the value found in part (b). This again involves an integration process where the integral's limits are adjusted to match half of the previous total charge. As with the previous parts, the calculation cannot be completed without the correct charge density expression.