A carbon dioxide laser emits a sinusoidal electromagnetic wave
that travels in vacuum in the negative x-direction. The wavelength
is 10.6 μm (in the infrared; see Fig. 32.4) and the
field is parallel
to the z-axis, with Write vector equations
for and as functions of time and position.
SOLUTION
IDENTIFY and SET UP: Equations (32.19) describe a wave traveling
in the negative x-direction with along the y-axis—that is, a
wave that is linearly polarized along the y-axis. By contrast, the
wave in this example is linearly polarized along the z-axis. At
points where is in the positive z-direction, must be in the positive
y-direction for the vector product x to be in the negative
x-direction (the direction of propagation). Figure 32.15 shows a
wave that satisfies these requirements.
EXECUTE: A possible pair of wave functions that describe the wave
shown in Fig. 32.15 are
The plus sign in the arguments of the cosine functions indicates
that the wave is propagating in the negative x-direction, as it
should. Faraday’s law requires that Emax = cBmax[Eq. (32.18)], so
Bmax =
=
=
To check unit consistency, note 1 V = 1 Wb/s that and 1 Wbm2 = 1T
We have so the wave number and angular
frequency are
We have λ= 10.6 x 10-6so the wave number and angular
frequency are
= 1.78 x 1014 rad/s
+(1.78× 1014 rad/s)t ]
MathML operators
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≤ ≤ ≤ To specify less than or equals