How can Maxwell's equations be used to derive electromagnetic wave phenomenon?

[Gear300]

For an electromagnetic wave, why is the electric field in phase with the magnetic field? As one increases in a given positive direction, so does the other (also in a given positive direction). I was somewhat expecting them to be slightly out of phase for some reason.

If its not too much to ask...can anyone provide a post showing the mathematics for deriving electromagnetic wave phenomenon from Maxwell's equations...sort of looking for them

 

[granpa]

who says they are in phase?

 

[Gear300]

I see...so they are not necessarily in phase...could you clarify (or provide the math)?

 

[jtbell]

If its not too much to ask...can anyone provide a post showing the mathematics for deriving electromagnetic wave phenomenon from Maxwell's equations...sort of looking for them

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxsup.html#c2