The degrees of freedom of an electromagnetic system are the values of
the electric and magnetic fields at all points 
in space,
and 
. We
therefore now deal with a much more complex system where we now have
to specify two vector fields for each point in space.
Again, we make the simplification of a plane wave and take the
direction of propagation to be x. This means that all points with
the same value of x will have the same electric and magnetic fields,
regardless of the values of y and z.
Mathematically, 
and 
.
Thus, the degrees of freedom are the value of these two fields for
each x,
The solution, then, must be something which gives the value of the degrees of freedom at all times t and so has the appearance
