So-called polarization horns appear in electromagnetic well logs when the sondes move through the interface between formations of different conductivities. Since the early 1990s, peaks in the logs have been attributed to the influence of surface charges due to the presence of electric field components perpendicular to the interfaces. A new analysis finds that surface charges should not be pinpointed as the immediate cause for the appearance of interface peaks in electromagnetic logs from any tool operating in any frequency range. This is accomplished by calculating the derivatives of the magnetic field components with respect to the sonde’s vertical position as it crosses the interface between two homogeneous isotropic media. The mathematical expressions reveal the components with smooth transitions and the ones with discontinuities in their rates of change across the interface. The analysis is applied to the four components needed to simulate the responses of coaxial and coplanar coil configurations in dipping logs. The results show that only the horizontal field from a horizontal dipole source suffers an influence from the current density field perpendicular to the interface between the two media, which gives rise to surface charges, but even for this component, the nonsmooth transitions are not associated with the perpendicular current. An anisotropic example gives further support to the conclusion that the polarization horns are associated with the discontinuous current density field parallel to the interface rather than with the continuous current across the interface.