1. Today’s agenda:
Electromagnetic Waves.
Energy Carried by Electromagnetic Waves.
Momentum and Radiation Pressure of an Electromagnetic Wave.

2. Today’s lecture is brought to you by the letter P.
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 tomorrow’s homework (if needed) (32.26)
where dp is the momentum carried in the volume dV.
Today’s lecture is brought to you by the letter P.

3. Maxwell showed that the momentum change of the object is then:
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:
incident
The direction of the momentum change of the object is in the direction of the incident radiation.

4. 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.
incident
reflected
The direction of the momentum change of the object is again in the direction of the incident radiation.

5. (Equations on this slide involve magnitudes of vector quantities.)
Radiation Pressure
The radiation pressure on the object is the force per unit area:
From Newton’s 2nd Law (F = dp/dt) we have:
For total absorption,
incident So
(Equations on this slide involve magnitudes of vector quantities.)

6. Today’s lecture is brought to you by the letter P.
This is the instantaneous radiation pressure in the case of total absorption:
For the average radiation pressure, replace S by <S>=Savg=I:
Electromagnetic waves also carry momentum through space with a momentum density of Saverage/c2=I/c2. This is not on your equation sheet but you have special permission to use it in tomorrow’s homework, if necessary.
Today’s lecture is brought to you by the letter P.

7. Using the arguments above it can also be shown that:
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 Prad=I/c on the emitter.

8. That’s because today’s lecture is brought to you by the letter P.
Example: a satellite orbiting the earth has solar energy collection panels with a total area of 4.0 m2. If the sun’s 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 earth’s 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!
That’s because today’s lecture is brought to you by the letter P.

9. Revolutionary Application of Electromagnetic Waves
I know you are mostly engineers, and think applications are important…
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*2014 price

10. New starting equations from this lecture:
There are even more on your starting equation sheet; they are derived from the above!