Today

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Todays agenda Electromagnetic Waves. Energy
Carried by Electromagnetic Waves. Momentum and
Radiation Pressure of an Electromagnetic Wave.
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Momentum and Radiation Pressure
EM waves carry linear momentum as well as energy.
The momentum density carried by an
electromagnetic wave is
This equation is not on your equation sheet, but
you have permission to use it for tomorrows
homework (if needed) (32.26)
where dp is the momentum carried in the volume
dV.
Todays lecture is brought to you by the letter P.
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When the momentum carried by an electromagnetic
wave is absorbed at a surface, pressure is
exerted on that surface.
If we assume that EM radiation is incident on an
object for a time ?t and that the radiation is
entirely absorbed by the object, then the object
gains energy ?U in time ?t.
Maxwell showed that the momentum change of the
object is then
The direction of the momentum change of the
object is in the direction of the incident
radiation.
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If instead of being totally absorbed the
radiation is totally reflected by the object, and
the reflection is along the incident path, then
the magnitude of the momentum change of the
object is twice that for total absorption.
The direction of the momentum change of the
object is again in the direction of the incident
radiation.
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Radiation Pressure
The radiation pressure on the object is the force
per unit area
From Newtons 2nd Law (F dp/dt) we have
For total absorption,
So
(Equations on this slide involve magnitudes of
vector quantities.)
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This is the instantaneous radiation pressure in
the case of total absorption
For the average radiation pressure, replace S by
ltSgtSavgI
Electromagnetic waves also carry momentum through
space with a momentum density of
Saverage/c2I/c2. This is not on your equation
sheet but you have special permission to use it
in tomorrows homework, if necessary.
Todays lecture is brought to you by the letter P.
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incident
absorbed
Using the arguments above it can also be shown
that
incident
reflected
If an electromagnetic wave does not strike a
surface, it still carries momentum away from its
emitter, and exerts PradI/c on the emitter.
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Example a satellite orbiting the earth has solar
energy collection panels with a total area of 4.0
m2. If the suns radiation is incident
perpendicular to the panels and is completely
absorbed find the average solar power absorbed
and the average force associated with the
radiation pressure. The intensity (I or
Saverage) of sunlight prior to passing through
the earths atmosphere is 1.4 kW/m2.
Assuming total absorption of the radiation
Caution! The letter P (or p) has been used in
this lecture for power, pressure, and momentum!
Thats because todays lecture is brought to you
by the letter P.
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Revolutionary Application of Electromagnetic Waves
I know you are mostly engineers, and think
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revolutionary new application that uses electro-
magnetic waves.
The UFO Detector. Only 48.54 at amazon.com (just
search for ufo detector).
The UFO detector continually monitors its
surrounding area for any magnetic and
electromagnetic anomalies.
2014 price
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New starting equations from this lecture
There are even more on your starting equation
sheet they are derived from the above!