A Unit Amplitude Polarized EM Wave Solution?

[ncholland]

A "unit magnitude" EM Wave?

Homework Statement

Write down the solution of Maxwell's equations corresponding to a plane polarised EM wave of unit amplitude and wavelength λ=2∏m, polarised in the zy plane and traveling in vacuo in the minus y direction.

Homework Equations

∇.E = 0
∇.B = 0
∇xE = -dB/dt
∇xB = με(dE/dt)
(they're meant to have subscript noughts...)

The Attempt at a Solution

Ok, so polarised in zy plane means E in z direction, B in x direction. λ=2∏m, combined with the fact that the speed is c, gives (1/m(y+ct)) as the argument.

So I have E=zcos(1/m(y+ct)) and b=x(1/c)cos(1/m(y+ct))
(z and x meant to be unit vectors) since there has to be a factor 1/c between their amplitudes...

Now this is probably a really stupid question, but what exactly does "unit amplitude" mean? Because, I mean, there are two waves - E and B. And if E has unit amplitude then B has amplitude 1/c...

 

[jbsteele]

but then, what if I wanted to keep the same amplitude for both, instead of having one unit and one 1/c? (I'm probably making it too complicated).Thanks for any help!