Are the E and B fields in phase in an EM wave?

[john b]

I keep looking at a sketch of the mutually perpendicular electric & magnetic fields in an EM wave. The sketch (and my text) says they are in phase, i.e. their maximum values occur simultaneously, ...

...but the discussion centers around the changing E field producing the B field and vice-versa. My gut tells me that the B field then should be a maximum when the E field is changing most rapidly, i.e. NOT at its max value. I think that discussion in the book also says that the energy is stored alternately in the E and B -- analogous with the kinetic and potential energy in SHM.

Both of these thoughts make me want to say that the maximum valuse should be out of phase -- where I am thinking incorrectly? Thanks

 

[Phrak]

When the E field changes the most rapidly with time, the magnetic field changes most rapidly along it direction of travel, and the converse.

$$\frac{\Delta E}{\Delta t} = \frac{\Delta B}{\Delta s}$$

 

[john b]

When the E field changes the most rapidly with time, the magnetic field changes most rapidly along it direction of travel, and the converse.

$$\frac{\Delta E}{\Delta t} = \frac{\Delta B}{\Delta s}$$

The classic picture I'm talking about is a graph of E & B on a x-y-z axis with the two sinosoidal curves in phase and perpendicular -- is it correct then to say, that the maximum values of E & B occur, at one instant, at the same locations along the Z axis but, if I graphed the fields at one location as a function of time, the maximum values would be 180deg out of phase?