In a parallel plane waveguide, electromagnetic waves propagate along the guide's direction, bouncing back and forth between the two parallel conducting plates. At the surface of the waveguide, there is no electric field component that is tangential to the surface. This phenomenon is known as the transverse electric (TE) mode, which is a specific mode of wave propagation in waveguides.
The TE mode is characterized by the fact that the electric field vector is perpendicular (transverse) to the direction of propagation. In this mode, the electric field lines are parallel to the conducting plates and do not cross them. Consequently, at the surface of the waveguide, the tangential component of the electric field (E_tangential) is zero because the electric field lines are running parallel to the surface and not crossing it.
Mathematically, this can be expressed as:
E_tangential = 0
This condition arises due to the boundary conditions imposed by the conducting plates of the waveguide. The conducting plates act as perfect electrical conductors, meaning that the electric field is not allowed to penetrate the plates. As a result, the tangential component of the electric field is forced to be zero at the surface.
It's important to note that in the TE mode, there is still a non-zero normal component of the electric field (E_normal) perpendicular to the surface. This component is responsible for the wave propagation along the waveguide's direction and is not affected by the conducting plates.