The
magnetic field equations for an electromagnetic wave in free space
are
|
Solution: Click For PDF Version (a)
A plane wave
characterised by angular frequency
The direction
of propagation of the wave is that of the propagation vector
We are given an electromagnetic wave in free space whose magnetic field equations are
From these functions, we note that the propagation vector for this wave is
Therefore, the direction of propagation of the wave is the negative y-direction. (b)
We know that
the electric field
The magnetic
field of the wave is in the direction of the unit vector
The Maxwell’s equation connecting the electric and magnetic fields that we can use is
Therefore, we have
and
The other
components of the electric field of the wave are
(c)
As the
polarization of the wave is determined by its electric field vector
|
,
.
We have to find (a)
the direction of propagation; (b)
write the electric field equation; and
(c) find whether the wave is polarized,
and, if
so, find its
direction.
and propagation vector
can
be described by the function
.
,
where
is the unit vector in the y-direction.
,
the magnetic field
,
and the Poynting vector
,
which is in the direction of the propagation vector
.
,
and its Poynting vector is in the direction
,
the electric field vector has to be in the direction
.
In other words the non-zero component of the electric field of the
wave will be
.
.
,
