Final answer:
To find the electric field at a cube's corner caused by a point charge at its center, Gauss's law for electric flux and Coulomb's law are applied, taking into account the symmetry of the problem and calculating the vector sum.
Step-by-step explanation:
The question asks to determine the electric field at a corner of a cube caused by a point charge located at the center of the cube. To solve this problem, we can employ Gauss's law and Coulomb's law. The electric flux, Φ, through a closed surface is equal to the enclosed charge divided by the permittivity of free space, Φ = q/ε0. Since the charge q is symmetrically located at the cube's center, the flux through each face of the cube is the same and is 1/6th of the total flux.
However, the electric field at a corner of the cube isn't obtained directly from electric flux; instead, we must use Coulomb's law to find the vector sum of the electric fields due to the point charge, projected onto the line from the charge to the corner. By considering symmetry, this can be found as E = (kq/r2) √3, where r is the distance from the charge to the corner of the cube and k is Coulomb's constant.