Illustration 32.3: Electromagnetic Plane Waves
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Electromagnetic waves (such as radio waves) can sometimes be approximated as plane waves if the observer is located far from the source. But what, exactly, does this plane wave look like? Before you begin, we should point out that plane waves are (like point masses) an idealization. Typical electromagnetic waves are not plane waves, not because they are curved (although they usually do have some curvature), but because they contain many frequencies and because they originate from more than one source. Although radio waves approximate a plane wave, visible light usually does not, unless it is produced by a laser. Because waves can be constructed by adding together multifrequency plane waves, understanding this Illustration is a good place to start. Restart.
The animation shows a plane electromagnetic wave's electric field. The magnetic field is not shown. Click-drag inside the large panel before you play the animation. What do you see? The lines pointing away from the z axis represent the electric field as measured along the axis. Move the slider. The slider controls the position (given in meters) of the transparent square. The transparent square represents the plane (hence the name plane wave) in which you are viewing the electric field in the right panel. Use the slider to estimate the wavelength. Play the animation. Note the animation time (given in nanoseconds) in the right-hand panel. What is the frequency of the wave? In what portion of the electromagnetic spectrum is the wave? Since the period is 6.68 x 10-8 s, the frequency is one over this or about 1.5 x 107 Hz, or 15 MHz. Since c = 3 x 108 m/s = λ f, this means that λ = c/f = 20 m, which is a radio wave.
The vectors along the z axis show the electric field along this path. What does the electric field in the xy plane look like for a particular value of z? Remember it is a plane wave. Move the square and notice that all points within the square have the same electric field, hence the name electromagnetic plane wave.
Notice that the wave equation for a pressure wave, P(x, t) = A sin(k x - ω t), traveling in the x direction could be changed to describe this electromagnetic plane wave (traveling in the z direction) as E(z, t) = Emax sin(k x - ω t) i. Why does the electric field vector have a component in the x direction but not in the z direction? Maxwell's equations tell us that the electromagnetic wave is a transverse wave. Therefore, unlike the pressure wave, the electromagnetic wave cannot have a component in the direction of propagation.
Note that k = 2π/λ and ω = 2πf so that v = ω/k = λf, where v is the wave speed, λ is the wavelength, and f is the frequency.
Illustration authored by Melissa Dancy and Wolfgang Christian.