Why are the electric and magnetic fields in phase in EM waves?

Consider a radio wave emanating from a dipole antenna. Close to the antenna, I would think the electric and magnetic fields would be 90 degrees out of phase (i.e. if the strength of the magnetic field is due to the rate of change in electric field, the maximum magnetic field strength should be between the peaks of the electric field when current flow is ). But as the wave radiates, the electric and magnetic field are thought to be in phase. How and why does this transition come about? Is it due to the inductance/capacitance of free space?