Yes, there is a phase shift between the electric field (E) and magnetic field (B) in a transverse electric (TE) wave propagating in a waveguide.
In a TE wave, the electric field is perpendicular to the direction of propagation and is confined within the waveguide. The magnetic field, on the other hand, has both a longitudinal component parallel to the direction of propagation and a transverse component perpendicular to it.
As the TE wave propagates, the electric and magnetic fields oscillate in time. The relationship between the electric and magnetic fields in terms of their amplitudes and phase can be described by Maxwell's equations. Specifically, the wave equation for TE waves in a waveguide reveals that there is a phase shift between the electric and magnetic fields.
The exact phase relationship depends on the specific geometry and mode of the waveguide, but in general, the electric and magnetic fields have a phase difference of 90 degrees (π/2 radians) in a TE wave. This means that when the electric field reaches its maximum (or minimum) value, the magnetic field is at its zero value, and vice versa.
It's important to note that this phase shift is specific to TE waves and the transverse nature of the fields in a waveguide. In other types of waves or propagation scenarios, the phase relationship between electric and magnetic fields may be different.