Final answer:
To calculate the total charge within the given volume, one needs to perform a triple integral of the charge density function over the specified limits for x, y, and z.
Step-by-step explanation:
The student's question involves calculating the total charge Q within a given volume with a non-uniform charge density that varies with x, y, and z coordinates. Since the charge density is not constant, we need to compute the total charge by integrating the given charge density ρ over the specified volume within the given limits.
The charge density function is ρ(x, y, z) = 5e⁻²ˣyz² nC/m³, with the bounds -2 ≤ x ≤ 2, 0 ≤ y ≤ 1, and 0 ≤ z ≤ 4. To find the total charge, we integrate this function over the entire volume:
Q = ∫ ∫ ∫ ρ(x, y, z) dx dy dz
The limits of integration for x are -2 to 2, for y are 0 to 1, and for z are 0 to 4. The integral can be solved by evaluating the triple integral successively for each variable, starting with the innermost integral and moving outward to the outermost integral.
Performing this integration gives us the value of total charge Q inside the specified volume.