We consider the possibility of standing electromagnetic waves
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Solution: Click For PDF Version We describe the standing electromagnetic waves by the functions
From these functions we obtain the following partial derivatives:
We require that the partial derivates of the E and B fields satisfy the relations
We note that we get the equations
and
These equations will be satisfied provided
where c is the speed of electromagnetic waves in vacuum. Therefore,
(b)
Assuming that
the
(c) Time average of S will be
(d) There is no flow of energy along the length and we have standing waves.
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is
suitably related to
and
is suitably related to
k. (b) We
have to find the (instantaneous)
Poynting vector. (c)
We have to show the time-average power flow
across any area is zero. (d) We
have to describe the flow of energy in this situation.
and
fields are perpendicular, the magnitude of the Poynting vector S
will be given by the expression
