# A unit magnitude EM Wave?

1. Nov 21, 2012

### ncholland

A "unit magnitude" EM Wave?

1. The problem statement, all variables and given/known data
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 travelling in vacuo in the minus y direction.

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

3. 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...

Last edited: Nov 21, 2012