# Plane EM wave in a vacuum, quick identity question…

Okay the question is, given a plane electromagnetic wave in a vacuum given by

**E**=(Ex,Ey,Ez)exp[itex]^{(i(k_{x}x+k_{y}y+k_{z}z-wt)}[/itex] and**B**=(Bx,By,Bz)exp[itex]^{(i(k_{x}x+k_{y}y+k_{z}z-wt)}[/itex] ,*where***k**= (kx,ky,kz),**to show that****k**X**E**=w**B**.So I’m mainly fine with the method. I can see the maxwell’s equaion ∇X**E**=-d**B**/dt, is the equation required.

-d**B**/dt=iw**B**.

And using ∇X**E**=i**k**X**E**, [1], the result follows.

My question is identifying equation [1]. How do you deduce this? Is it supposed to be obvious in any way. (*I’ve done a check on the LHS and RHS so I can see its true*), but should this be obvious?

**Thanks in advance for your assistance .**

http://ift.tt/1cNqRDj

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