1
Lecture 32
Energy and momentum
Energy and momentum.
Standing waves.
Energy in a EM wave
Energy density due to an electric field:
2
0
1
2
u
E
Energy density due to a magnetic field:
2
0
1
2
u
B
Energy density for an EM wave:
2
2
0
0
1
1
2
2
u
E
B
but
0
0
B
E
cB
2
2
0
0
0
0
1
1
2
2
u
E
E
2
0
u
E
Energy density equally
split between
E, B
fields
Energy transport
How much energy goes through
a surface of area
A
in time
dt
?
Energy in this “box”:
y
x
propagation
cdt
2
dU
udV
E Acdt
z
0
Energy flow per unit time and per unit area:
2
0
1
dU
S
cE
A dt
0
EB
Definition:
Poynting vector
0
1
S
E
B
Energy flow per unit
time and per unit area
I
S
Intensity:
ACT: Plane harmonic wave
P
At the time shown, the magnetic
field at point P (on the
y
axis) is:
1.
B
max
i
2.
B
max
j
3.
0
0%
0%
0%
60
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2
x
y
Propagation
P
At the time shown, the magnetic
field at point P (on the
y
axis) is:
A.
B
max
i
B.
B
max
j
C.
0
z
x
z
y
E/B
are the same at all points
in each
yz
plane!
Propagation direction is
,
so
is in the
direction
and
is in the
direction
E
B
E
x
B
y
Energy in the harmonic wave
2
max
max
1
1
ˆ
ˆ
cos
S
E
B
E
B
kx
t
j
k
max
ˆ
cos
E
E
kx
t j
max
ˆ
cos
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 Spring '07
 Johnson
 Physics, Energy, Momentum, Light, Wavelength

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