Proving E and B are orthogonal

E . B =0

∇xE=B

The Attempt at a Solution

I know AxB=C implies both A and B are orthogonal to C but does the same thing ring true for the Del cross something? In any case, is there a nice simple proof for the problem stated? This is not HW by the way but seems to be a bit homeworish

WannabeNewton
You're going to have to be way more detailed. I'm assuming E and B are the electric and magnetic field respectively. If so, then in general they are not orthogonal. For special solutions to Maxwell's equations they can be orthogonal, such as for vacuum radiation fields, but it is certainly not true in full generality.

You're going to have to be way more detailed. I'm assuming ##E## and ##B## are the electric and magnetic field respectively. If so, then in general they are not orthogonal. For special solutions to Maxwell's equations they can be orthogonal, such as for vacuum radiation fields, but it is certainly not true in full generality.

ah, for it to be light must they be orthogonal?

WannabeNewton
Have you seen vacuum plane wave solutions to Maxwell's equations before?

Have you seen vacuum plane wave solutions to Maxwell's equations before?

yes it says this must be the case. For light. I guess this means E.B=0 for light but it is not necessary for them to be orthogonal, but this does not mean it is light if the first condition is not met?