OK. First, we should just state the form of the 'wave equations'. These have a lot of interesting physics behind them, but for now we'll just state them!
Say the light wave travelling in the -direction, in free space. Then, say the wave is polarised, so the electric field is in the -direction. Then the only non-zero components of the fields are and :
Now, an explanation of the symbols I've used:
In your question, you have been given the following information:
- is the wavenumber (or wavevector) of the wave. It's defined by , where is the wavelength.
- is the angular frequency of the wave. It has units of "radians per second", and relates to the 'true' frequency by .
- is the speed of light.
and so you can calculate
( is a unit, the tesla.)
Put these into the expressions above, and ignoring the units, you get:
- - -
Your answers are written slightly diffierently: they have a minus sign, . This doesn't matter. However, I seem to have a different answer for (I don't know why!)
Also, the form used in Wikipedia has an "extra" phase factor ; I have made . You can do this just by choosing the origin of your coordinates in the right place!