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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Energy Carried by Electromagnetic Waves
This is derived from Maxwells equations.
The magnitude S represents the rate at which
energy flows through a unit surface area
perpendicular to the direction of wave
propagation (energy per time per area).
Thus, S represents power per unit area. The
direction of S is along the direction of wave
propagation. The units of S are J/(sm2) W/m2.
J. H. Poynting, 1884.
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y
E
S
x
Because B E/c we can write
c
B
z
These equations for S apply at any instant of
time and represent the instantaneous rate at
which energy is passing through a unit area.
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EM waves are sinusoidal.
EM wave propagating along x-direction
The average of S over one or more cycles is
called the wave intensity I.
The time average of sin2(kx - ?t) is ½, so
Notice the 2s in this equation.
This equation is the same as 32-29 in your text,
using c 1/(?0?0)½.
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Thus,
Note Saverage and ltSgt mean the same thing!
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Energy Density
The energy densities (energy per unit volume)
associated with electric and magnetic fields are
Using B E/c and c 1/(?0?0)½ we can write
remember E and B are sinusoidal functions of time
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For an electromagnetic wave, the instantaneous
energy density associated with the magnetic field
equals the instantaneous energy density
associated with the electric field.
Hence, in a given volume the energy is equally
shared by the two fields. The total energy
density is equal to the sum of the energy
densities associated with the electric and
magnetic fields
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instantaneous energy densities (E and B vary with
time)
When we average this instantaneous energy density
over one or more cycles of an electromagnetic
wave, we again get a factor of ½ from the time
average of sin2(kx - ?t).
and
Recall
so we see that
The intensity of an electromagnetic wave equals
the average energy density multiplied by the
speed of light.
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Help!
These factors of ¼, ½, and 1 are making my brain
hurt!
Its really not that bad.
Its really not that bad. These are the energy
densities associated with E(t) and B(t) at some
time t
Add uB and uE to get the total energy density
u(t) at time t
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Help!
Again, these are the energy densities associated
with E(t) and B(t) at some time t
If you average uB and uE over one or more cycles,
you get an additional factor of ½ from the time
average of sin2(kx-?t).
The Emax and Bmax come from writing E Emax
sin(kx-?t) and B Bmax sin(kx-?t), and
canceling the sine factors.
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Help!
These are the average energy densities associated
with E(t) and B(t) over one or more complete
cycles.
Add ?uE? and ?uB? to get the total average energy
density over one or more cycles
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Help!
Summary
If you use a starting equation that is not valid
for the problem scenario, you will get incorrect
results!