You may wish to review Sections 16.4 and 16.8 on the trans- port of energy by string waves and sound. Figure P33.46 is a graphical representation of an electromagnetic wave mov- ing in the x direction. We wish to find an expression for the intensity of this wave by means of a different process from that by which Equation 33.27 was generated. (a) Sketch a graph of the electric field in this wave at the instant t = 0, letting your flat paper represent the xy plane. (b) Compute Figure P33.46 the energy density u in the electric field as a function of x at the instant t = 0. (c) Compute the energy density in the magnetic field uz as a function of x at that instant. (d) Find the total energy density u as a function of x, expressed in terms of only the field amplitude. (e) The energy in a “shoebox" of length A and frontal area A is E, = S uA dx. electric (The symbol E, for energy in a wave- length imitates the notation of Section 16.4.) Perform the integration to of A, A, Ear and universal constants. (f) We may think of the energy transport by the whole wave as a series of these shoeboxes going past as if carried on a conveyor belt. Each shoebox passes by a point thea amount of this energy in terms What is of greater interest for a sinusoidal plane electromagnetic wave is the time average of S over one or more cycles, which is called the wave intensity I. (We discussed the intensity of sound waves in Chapter 16.) When this average is taken, we obtain an expression involving the time average of cos? (kx – wt), which equals . Hence, the average value of S (in other words, the intensity of the wave) is in a time interval defined as the period T = 1/f of the wave. Find the power the wave car- ries through area A. (g) The intensity of the wave is the power per unit area through which the wave passes. Com- pute this intensity in terms of E_ and universal constants. (h) Explain how your result compares with that given in F2 max cB I = S = avg (33.27) Equation 33.27.
You may wish to review Sections 16.4 and 16.8 on the trans- port of energy by string waves and sound. Figure P33.46 is a graphical representation of an electromagnetic wave mov- ing in the x direction. We wish to find an expression for the intensity of this wave by means of a different process from that by which Equation 33.27 was generated. (a) Sketch a graph of the electric field in this wave at the instant t = 0, letting your flat paper represent the xy plane. (b) Compute Figure P33.46 the energy density u in the electric field as a function of x at the instant t = 0. (c) Compute the energy density in the magnetic field uz as a function of x at that instant. (d) Find the total energy density u as a function of x, expressed in terms of only the field amplitude. (e) The energy in a “shoebox" of length A and frontal area A is E, = S uA dx. electric (The symbol E, for energy in a wave- length imitates the notation of Section 16.4.) Perform the integration to of A, A, Ear and universal constants. (f) We may think of the energy transport by the whole wave as a series of these shoeboxes going past as if carried on a conveyor belt. Each shoebox passes by a point thea amount of this energy in terms What is of greater interest for a sinusoidal plane electromagnetic wave is the time average of S over one or more cycles, which is called the wave intensity I. (We discussed the intensity of sound waves in Chapter 16.) When this average is taken, we obtain an expression involving the time average of cos? (kx – wt), which equals . Hence, the average value of S (in other words, the intensity of the wave) is in a time interval defined as the period T = 1/f of the wave. Find the power the wave car- ries through area A. (g) The intensity of the wave is the power per unit area through which the wave passes. Com- pute this intensity in terms of E_ and universal constants. (h) Explain how your result compares with that given in F2 max cB I = S = avg (33.27) Equation 33.27.
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Transcribed Image Text:You may wish to review Sections 16.4 and 16.8 on the trans-
port of energy by string waves and sound. Figure P33.46 is a
graphical representation of an electromagnetic wave mov-
ing in the x direction. We wish to find an expression for the
intensity of this wave by means of a different process from
that by which Equation 33.27 was generated. (a) Sketch a
graph of the electric field in this wave at the instant t = 0,
letting your flat paper represent the xy plane. (b) Compute
Figure P33.46
the energy density u in the electric field as a function
of x at the instant t = 0. (c) Compute the energy density
in the magnetic field uz as a function of x at that instant.
(d) Find the total energy density u as a function of x,
expressed in terms of only the field amplitude.
(e) The energy in a “shoebox" of length A and frontal area
A is E, = S uA dx.
electric
(The symbol
E, for
energy in a wave-
length imitates the notation of Section 16.4.) Perform the
integration to
of A, A, Ear and universal constants. (f) We may think of
the energy transport by the whole wave as a series of these
shoeboxes going past as if carried on a conveyor belt. Each
shoebox passes by a point
thea
amount of this energy in terms
What is of greater interest for a sinusoidal plane electromagnetic wave is the
time average of S over one or more cycles, which is called the wave intensity I. (We
discussed the intensity of sound waves in Chapter 16.) When this average is taken,
we obtain an expression involving the time average of cos? (kx – wt), which equals .
Hence, the average value of S (in other words, the intensity of the wave) is
in a time interval defined as the
period T = 1/f of the wave. Find the power the wave car-
ries through area A. (g) The intensity of the wave is the
power per unit area through which the wave passes. Com-
pute this intensity in terms of E_ and universal constants.
(h) Explain how your result compares with that given in
F2
max
cB
I = S =
avg
(33.27)
Equation 33.27.
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