Discussion
Consider an ideal rectangular wave guide (dimension ~ 4.0 cm × 2.0 cm) with vacuum inside. Plane monochromatic electromagnetic radiation having a wavelength of 6 cm is introduced in this wave guide. The radiation propagates inside the wave guide in mode :
Answer: A
The radiation propagates in Only TE10 mode.
A mode propagates only if the free-space wavelength is shorter than its cut-off wavelength. For a guide with \(a = 4\) cm and \(b = 2\) cm:
- TE10: \(\lambda_{c} = 2a = 8\) cm, longer than 6 cm, so it propagates.
- TE01: \(\lambda_{c} = 2b = 4\) cm, shorter than 6 cm, so it is cut off.
- TM modes need both indices non-zero; TM10 does not exist, and TM11 has \(\lambda_{c} \approx 3.6\) cm.
So only the dominant TE10 mode carries the 6 cm radiation.
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