Animation 1
The fundamental TE 10 mode in a rectangular waveguide has three nonzero field components: (1) E y, which has a sine distribution across the width of the guide (x-direction)—it is the strongest in the middle and tapers off toward the sidewalls; (2) H x, which also has a sine distribution in the x-direction; and (3) the longitudinal H z component, which has a cosine dependence on x—it is the strongest at the sidewalls. These components are sketched in the cross-section plot below:
Figure 1 : Field in the cross-section of the waveguide.
Here are some views of the field in a rectangular waveguide of cross-section 60 by 25 mm (generated with the High-frequency Structure Simulator, HFSS, of Ansoft Corp.) The periodic structure of the field in Figures 4, 5 and 6 is obvious: the patterns repeat with every wavelength λ .

Figure 2 : E-vector in the cross-section.

Figure 3 : H-vector in the cross-section.
Figure 4 : E and H vector intensity along the waveguide, side view: there is no difference except for the scale, as expected.

Figure 5 : H-vector along the waveguide, top view.

Figure 6 : E and H along the waveguide, top view.
Observe a traveling wave in the waveguide in terms of its electric field intensity (generated with MEFiSTo3D-Pro of Faustus Scientific).

Animation 1 : E and H along the waveguide, top view.
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