A point charge \(q\) is located on the central symmetry axis of a flat circular disk of radius \(R\), at a distance \(d\) from the center of the disk. An open hemispherical surface shares the same circular boundary as the disk, forming a closed surface that encloses no electric charge. In terms of given quantities and fundamental constants, which of the following expressions represents the magnitude of the electric flux \(\Phi_E\) through the open hemispherical surface?