Final answer:
The electric flux through one face of a cube with a point charge q at the center is found using Gauss's law. The total flux through the entire cube is q/ε0, and since the flux is distributed equally across all six faces, the flux through one face is (q/ε0)/6.
Step-by-step explanation:
If a point charge q is located at the center of a cube with sides of length a, the electric flux through one face of the cube can be found using Gauss's law. Gauss's law states that the total flux out of a closed surface is equal to the charge enclosed divided by the permittivity of free space (also known as the electric constant ε0).
Since the charge is symmetrically located at the center of the cube, the flux will be evenly distributed through each of the six faces of the cube. The total flux through the cube is given by Φtotal = q/ε0. As the cube has six faces, the flux through any one face will be one-sixth of the total flux and is given by Φ = (q/ε0)/6.
It is important to realize that the electric flux through each face is unaffected by the shape or size of that surface, as long as the surface encloses the charge q. For a simplified result, if the values are provided or needed for calculations, the numeric value for the charge q and the electric constant ε0 should be substituted into the formula.