# Phase relation between current and electromagnetic field generated

 Sci Advisor PF Gold P: 1,777 From Maxwell's Equations, for a time-harmonic field the electric field it appears that it may lead the current by 90 degrees since the time derivative of the electric field is equal to the curl of the magnetic field and the source current. But this is only at the source point, due to the retardation of the fields, there is another phase shift that arises as the fields propagate. Let us take the z component of the electric field from a z directed point source current. The field for a unity current source is: $$E_z = \frac{i\omega\mu}{4\pi k^2} \left[ ik - \frac{1+k^2z^2}{r^2} - \frac{3ikz^2}{r^2} + \frac{3z^2}{r^3} \right] \frac{e^{ikr}}{r^2}$$ So we find that different parts of the field are 90 degrees and 180 degrees out of phase of the current even before we take into account the spatial phase shift. As you go away from the source though, only the first term remains and you have a field that is 180 degrees out of phase plus a spatial phase shift. So in the situation where you have a waveguide, then you have to contend with the superposition of the reflections which would make it even more difficult. But my guess is you will have a hard time determining a rule for this.