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https://www.physicsforums.com/showthread.php?p=2881300#post2881300
According to the quoted thread above and according to textbooks and Wikipedia the phase between the E and B fields of an electromagnetic wave propagating in free space is zero. This assertion is based on the Maxwell equations using a planar wave.
DaleSpam rephrases Maxwell's laws in the quoted thread:
However, if the E-field is subject to an alternating displacement, the maximum and minimum field amplitudes occur when the rate of displacement is ##\frac{∂E}{∂t}=0##. According to the Maxwell equation
To continue with this, when the electric field is zero, the rate of change of the electric field is maximal and the curl of the magnetic field is maximal too, which leads to the conclusion that when the electric field does not exist (its rate of change is maxed), the magnetic field magnitude is maximal and rotational.
This goes against the interpretation of DaleSpam, which to me is solely based on a math interpretation, not a physical interpretation. I would conclude that there is a 90° phase difference and that therefore
According to the quoted thread above and according to textbooks and Wikipedia the phase between the E and B fields of an electromagnetic wave propagating in free space is zero. This assertion is based on the Maxwell equations using a planar wave.
DaleSpam rephrases Maxwell's laws in the quoted thread:
Wannabeagenius is correct. They are in-phase, not 90 degrees out of phase.
If you look at Maxwell's laws in vacuum you will find that it is not quite corect that "a changing magnetic field induces an electric field". It is more correct to say "a changing magnetic field induces curl of an electric field" or in other words "a changing magnetic field (in time) induces a spatially changing electric field". When you express it correctly you immediately see that the electric and magnetic fields should be in phase.
However, if the E-field is subject to an alternating displacement, the maximum and minimum field amplitudes occur when the rate of displacement is ##\frac{∂E}{∂t}=0##. According to the Maxwell equation
##∇ \times B=\frac{∂E}{∂t}##
the curl of the magnetic field is then zero when the electric field is maximal or minimal. If the curl of the magnetic field is zero, then my interpretation of what the curl means, leads to the conclusion that the magnetic field itself has a zero value.To continue with this, when the electric field is zero, the rate of change of the electric field is maximal and the curl of the magnetic field is maximal too, which leads to the conclusion that when the electric field does not exist (its rate of change is maxed), the magnetic field magnitude is maximal and rotational.
This goes against the interpretation of DaleSpam, which to me is solely based on a math interpretation, not a physical interpretation. I would conclude that there is a 90° phase difference and that therefore
##E=E_{0}sin(\omega t - kx)##
is incompatible with the Maxwell equations. Of course I might be completely wrong, yet DaleSpam's explanation does not cut it for me, unless my interpretation of the curl of a vector field is out of touch.