•
•
•
Thus, we obtain for Eq. (A.1b)
i.e. only the y component of the magnetic field survives. The electric and magnetic
components are related to each other via
By substituting Eq. (4.4) into Eq. (A.17), we find
where
is the impedance of free space.
In summary, we found the following properties of the electromagnetic field:
The electric and magnetic field vectors are perpendicular to each other and also
perpendicular to the propagation vector,
The electric and magnetic fields are proportional to the propagation direction,
hence electromagnetic waves are transverse waves.
The electric and magnetic vectors have a constant, material-dependent ratio. If
the electric field is along the x direction and the magnetic field is along the y
direction, this ratio is given by
where
is the impedance of free space.
The derivations in this section were done for plane waves. However, it can be shown
that the properties of electromagnetic waves summarized in the bullet points above are
valid for electromagnetic waves in general.