Describe the principle of guided wave propagation in a rectangular waveguide. Derive the expression for the cut-off frequency of modes in terms of waveguide dimensions.
Guided wave propagation in a rectangular waveguide refers to the controlled transmission of electromagnetic waves along a confined path defined by conducting walls. A rectangular waveguide consists of a hollow metallic structure with cross-sectional dimensions (a) (width) and (b) (height), where (a > b), and the wave propagates primarily along the longitudinal axis, usually designated as the (z)-axis. The metallic boundaries impose boundary conditions on the electric and magnetic fields, restricting the modes that can exist in the waveguide and determining their propagation characteristics. Unlike free-space propagation, guided waves in a waveguide do _____ _________ ___ ______ __________.
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Explain the Lorentz transformation between two inertial frames. Obtain the transformation laws for the electric and magnetic fields.
Derive the electromagnetic wave equation for and
fields in vacuum starting from Maxwell's equations. Discuss the general properties of plane electromagnetic waves, including their speed and polarisation.
Using boundary conditions on the electric and magnetic fields, derive the Fresnel reflection and transmission coefficients for a plane wave incident normally on a boundary between two dielectric media.
Starting from the scalar and vector potentials, derive the expression for the electromagnetic fields produced by a small oscillating electric dipole.
Describe the principle of guided wave propagation in a rectangular waveguide. Derive the expression for the cut-off frequency of modes in terms of waveguide dimensions.
Define the Poynting vector. Starting from Maxwell's equations, derive the Poynting theorem and explain its physical interpretation in terms of energy conservation in electromagnetic fields.
Show that if the electric field of the incident wave is normal to the plane of incidence, the electric fields of the reflected and transmitted waves are also normal to the plane of incidence.