A waveguide field with nonzero axial magnetic field component Hz described by Hz = C * cos(Bx) * cos(Ay) indicates which class of modes? (Assume standard rectangular waveguide mode definitions and boundary conditions.)

Introduction:
In rectangular waveguides, modes are categorized as TE (transverse electric) or TM (transverse magnetic) depending on whether the axial electric field Ez or the axial magnetic field Hz is zero. Recognizing which axial component exists identifies the mode family.

Given Data / Assumptions:

• Rectangular waveguide with conducting walls and standard boundary conditions.
• Field expression includes a nonzero Hz = C * cos(Bx) * cos(Ay).
• No claim that Ez is present; only Hz is explicitly nonzero.

Concept / Approach:

By definition: TE modes have Ez = 0 and generally Hz ≠ 0; TM modes have Hz = 0 and Ez ≠ 0. Therefore, the presence of a nonzero axial magnetic field (Hz) directly indicates a TE mode. The specific cosine dependence in x and y (with separation constants A and B) is consistent with standing field patterns that satisfy wall boundary conditions for a TE_mn mode.

Step-by-Step Solution:

Verification / Alternative check:

Solving Maxwell’s equations with conducting boundary conditions yields families TE_mn and TM_mn. For TE, the scalar potential solution is typically cast in terms of Hz; for TM, it is cast in terms of Ez. The given form matches the TE formulation.

Why Other Options Are Wrong:

• TM waves: would require Hz = 0, contradicting the given.
• Both / Some of each: a single field solution cannot simultaneously satisfy both Ez = 0 and Hz = 0 unless trivial; mode families are distinct.
• TEM in rectangular guides: not supported below cutoff because waveguides do not sustain a true TEM mode without a return path like in coax.

Common Pitfalls:

Confusing which component is zero for TE vs TM. Remember: “TE → Transverse Electric → Ez = 0.”

Final Answer:

TE waves