(a) Calculate the induced surface charge density TM and the longitudinal surface current density K TM...
Question:
(a) Calculate the induced surface charge density σTM and the longitudinal surface current density KTM associated with the propagation of a TM mode in a perfectly conducting waveguide with a uniform cross section. Show that KTM = νpσTMẑ where νp is the phase velocity of the wave propagating in the z-direction.
(b) Calculate the induced surface charge density σTE and the surface current density KTE associated with the propagation of a TE mode in a perfectly conducting waveguide with a uniform cross section. Show that ẑ · KTE = vgσTE where νg is the group velocity of the wave.
(c) Show that in the TE case a surface current appears in the transverse
direction also.(d) Show that the surface current and surface charge satisfy a “surface continuity equation” for both TE and TM modes.
Step by Step Answer:
a Surface charge density and longitudinal surface current density for TM mode For a TM Transverse Magnetic mode in a perfectly conducting waveguide wi...View the full answer
