PHYS5140 (2023-24 Term1)
Homework 5
Due: 11/11/2023 Sat (before 11:59 pm)
Submit your answers via Blackboard
Total marks= 70 (3 problems)
1. Consider an EM plane wave propagating in a conductor. Suppose its values of ε, μ and σ
are known.
(a) (16 marks) Calculate the time averaged energy density of the wave. Show that the
magnetic energy density term is always greater than the electric energy density term.
(b) (14 marks) Find the intensity of the wave in (a).
2. Consider the TM mode propagating in z-direction in an infinitely long hollow rectangular
waveguide made of perfect conductor. The cross section of the waveguide is shown below.
(a) (20 marks) Find the z-component of the electric field and the cutoff frequencies.
(b) (8 marks) Which mode that has the lowest possible cutoff frequency? Is it the same
that of the TE mode that has the lowest possible cutoff frequency?
3. (12 marks) Consider the setup in Qu.3 of homework 3. Using the electric and magnetic
field found in that problem, find the Poynting vector .