Waveguide mode property check: In a transverse-electric (TE) mode of a hollow waveguide, is the axial electric field component Ez equal to zero?

Introduction / Context:
Electromagnetic modes in hollow metallic waveguides are classified as TE or TM based on which longitudinal field component vanishes along the direction of propagation. This definition is central to deriving cutoff frequencies, field patterns, and boundary conditions for rectangular and circular waveguides.

Given Data / Assumptions:

• Hollow, perfectly conducting walls to simplify boundary conditions.
• Propagation along the axis, typically labeled z.
• Time-harmonic fields and standard separation of variables treatment.

Concept / Approach:

By definition, TE stands for transverse electric. In a TE mode, the electric field has no component along the axis of propagation, so Ez = 0. The magnetic field retains an axial component Hz that couples to the transverse fields via Maxwell curl equations. This holds whether the cross section is rectangular or circular and whether the waveguide is air filled or filled with a uniform dielectric.

Step-by-Step Solution:

Verification / Alternative check:

Mode charts list Ez = 0 for TEmn modes such as TE10 in rectangular waveguide. Practical field probes confirm a significant axial magnetic field but negligible axial electric field for TE modes, consistent with theory and measurement.

Why Other Options Are Wrong:

• False or conditional responses conflict with the definitional nature of TE.
• Filling the guide with a uniform dielectric changes phase velocity and cutoff but not the TE or TM definitions.

Common Pitfalls:

Confusing TE or TM with TEM. Hollow single conductor guides do not support a true TEM mode. Another pitfall is assuming a small Ez must exist in TE modes; by definition, it is zero in the ideal case.

Final Answer:

True