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

2. Momentum and Radiation Pressure EM waves carry linear momentum as well as energy. The momentum density carried by an electromagnetic wave is Today’s lecture is brought to you by the letter P. where dp is the momentum carried in the volume dV. This equation is not on your equation sheet, but you have permission to use it for tomorrow’s homework (if needed) (32.26)

3. 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. incident When the momentum carried by an electromagnetic wave is absorbed at a surface, pressure is exerted on that surface.

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

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

6. This is the instantaneous radiation pressure in the case of total absorption: For the average radiation pressure, replace S by =S avg =I: Electromagnetic waves also carry momentum through space with a momentum density of S average /c 2 =I/c 2. 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. incident reflected absorbed Using the arguments above it can also be shown that: If an electromagnetic wave does not strike a surface, it still carries momentum away from its emitter, and exerts P rad =I/c on the emitter.

8. Example: a satellite orbiting the earth has solar energy collection panels with a total area of 4.0 m 2. 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 S average ) of sunlight prior to passing through the earth’s atmosphere is 1.4 kW/m 2. 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.

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