Alternative derivations for the fields inside a waveguide

Generally, the longitudinal magnetic field of the transverse electric (TE) wave inside a waveguide is obtained by solving the corresponding Helmholtz wave equation, which further leads to the derivation of the remaining fields. In this paper, we provide an alternative way to obtain this longitudinal magnetic field by making use of one of the Maxwell’s equations instead of directly relying on the Helmholtz wave equation. The longitudinal electric field of the transverse magnetic (TM) wave inside a waveguide can also be derived in a similar fashion. These derivations, which are different from those found in the introductory textbooks on microwave engineering, make the study of waveguides more interesting.