Rectangular waveguides (propagation along z): What is the correct relationship of the axial field components Ez and Hz in TE and TM modes?
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AEz and Hz are both zero
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BIn TE mode Ez = 0 and in TM mode Hz = 0
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CIn TE mode Hz = 0 and in TM mode Ez = 0
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DIn both TE and TM modes both Ez and Hz are non-zero
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EEz = Hz = 0 only at cutoff
Answer
Correct Answer: In TE mode Ez = 0 and in TM mode Hz = 0
Explanation
Introduction / Context:Waveguide modes are categorized by which longitudinal field component vanishes. This classification governs boundary conditions and cutoff relations for rectangular guides used in microwave systems.
Given Data / Assumptions:
- Hollow, perfectly conducting rectangular waveguide.
- Propagation is along the z-axis.
- Steady-state sinusoidal fields.
Concept / Approach:
By definition: TE (transverse electric) implies Ez = 0 and Hz generally non-zero; TM (transverse magnetic) implies Hz = 0 and Ez generally non-zero. No true TEM mode exists in a single-conductor hollow waveguide.
Step-by-Step Solution:
Apply TE definition to set Ez = 0.Apply TM definition to set Hz = 0.Use boundary conditions on the walls to determine the transverse fields.Conclude the correct relationship: TE ⇒ Ez = 0; TM ⇒ Hz = 0.Verification / Alternative check:
Mode tables list Ez = 0 for TEmn and Hz = 0 for TMmn. Field probes in lab setups corroborate these properties for common modes like TE10.
Why Other Options Are Wrong:
- Both zero would imply TEM, which is unsupported in a hollow guide.
- Both non-zero violates TE/TM definitions.
- Cutoff-only conditions do not change the definitional property.
Common Pitfalls:
Confusing mode type with polarization; assuming a TEM mode exists in rectangular guides.
Final Answer:
In TE mode Ez = 0 and in TM mode Hz = 0