I. Guided waves A waveguide is a hollow conducting tube, such that the fields ca
ID: 2304552 • Letter: I
Question
I. Guided waves A waveguide is a hollow conducting tube, such that the fields can exist within the vacuum surrounded by conducting surfaces. Recall that for conductors, the electric field must be perpendicular or zero at the conducting surface, to first approximation. A. Suppose an electromagnetic plane wave with electric field polarized in Perspective view the 3 direction were sent into a rectangular waveguide as shown at right. 1. Does this wave satisfy the boundary condition on the top and bottomSide view of the waveguide? What about the front and back of the waveguide? Based on your answers above, is this plane wave a valid solution inside of the waveguide? 2. Are there any other polarizations for which a plane wave can propagate through the waveguide with k-k2? Explain your reasoning 3.Explanation / Answer
1) The wave is polarised along the x direction. This means that the electric field is vibrating along the x-y plane. This is obviously perpendicular to the top and bottom surfaces of the wave guide.
But the oscillations are parallel to the plane of the front and back of the wave guide. So, it is not satisfying the boundary conditions here.
2) Since it does not satisfy the boundary conditions, it is not a valid solution inside the waveguide.
3) Even if the polarisation vector is rotated, the condition is that the oscillations of the electric field in the wave be perpendicular to the sides of the rectangular wave guide. This gives us only two possible orientations for the polarisation- Vertical (x direction)and Horizontal(y direction). But , even if this condition is satisfied, the condition that it has to be perpendicular to the front and back will not be satisfied. Hence a plane EM wave cannot exist.
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P.S.:
TEM (Transvers Electromagnetic Waves) cannot exist in a wave guide (hollow, rectangular conducting surface).
That being said, transverse Electric waves and transverse Magnetic waves which can exist.
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