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Power Flow in Electromagnetic Waves
The timedependent power flow density of an electromagnetic wave
is given by the
instantaneous Poynting vector
For
timevarying fields
it is important to consider the
timeaverage
power flow density
where
T
is the period of observation.
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View Full Document Consider
timeharmonic fields
represented in terms of their phasors
The
timedependent Poynting vector
can be expressed as the sum
of the crossproducts of the components
The
timeaverage power flow density
can be obtained by integrating
the previous result over a period of oscillation
T
. The prefactors
containing field phasors do not depend on time, therefore we have
to solve for the following integrals:
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View Full Document The final result for the
timeaverage power flow density
is given by
Now, consider the following cross product of
phasor vectors
By combining the previous results, one can obtain the following
time average rule
We also call
complex Poynting vector
the quantity
NOTE:
the complex Poynting vector
is not
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This note was uploaded on 03/09/2012 for the course ECE 450 taught by Professor E.kudeki during the Spring '12 term at Illinois College.
 Spring '12
 E.Kudeki
 Electromagnet

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