A Hertz dipole radiating in the presence of a dihedral corner constitutes a 3-D wedge-diffraction problem. The first-order physical-optics (PO) solution developed in this paper applies to an obtuse-angled penetrable dihedral corner excited by an electric or magnetic dipole which is either parallel or normal to the edge. A charge distribution is introduced along the apex of the dihedral corner to account for the discontinuity of the PO approximation to the field on the faces at their common edge. Thus, a corrected PO solution is obtained. The integral expression for the field intensity at great distance from the edge is evaluated asymptotically. The resulting formula is uniformly valid and continuous across both shadow boundaries. The effect of the aforementioned charge distribution along the edge is highlighted through a reciprocity check. Maps of every constituent of the field over a coastal corner are presented for all four types of dipole source.