Final answer:
The electric flux through a cubical surface with a point charge at its center can be calculated using Gauss's Law. The total flux through the cube is the enclosed charge divided by the permittivity of free space, and the flux through one face is one-sixth of that total flux.
Step-by-step explanation:
The student's question pertains to calculating the electric flux through a cubical surface with a point charge at its center. According to Gauss's Law, the electric flux Φ through a closed surface is equal to the enclosed charge q divided by the permittivity of free space ε0. Hence, for a point charge q = +6.00 nC located at the center of a cube, the flux through the entire closed cubical surface is:
Φ = q / ε0
Substituting the given values (and using ε0 = 8.85 × 10-12 C2/N·m2):
Φ = (6.00 × 10-9 C) / (8.85 × 10-12 C2/N·m2)
Φ = 677.97 N·m2/C (approximately)
This is the flux through the entire cube. For (b), the flux through one of the six faces of the cube is simply one-sixth of the total flux, as the charge is symmetrically located at the center and the cube has six identical faces. Thus:
Φface = Φ / 6
Φface = 677.97 N·m2/C / 6
Φface = 112.99 N·m2/C (approximately)