Question

4. Consider the cylindrical waveguide below, which has an electromagnetic wave propagating in the space between the inner and outer conductors, which is a gap where air exists. The radius of the inner conductor is a, while the inner radius of the outer conductor is b (as shown). The fields in the air-gap have the form E = E0r cos (kz z ωt) B = B0r cos (kz z ωt) where E0 and B0 are constants, r is the radial distance from the symmetry axis of the wire (with a < r < b signifying the air-filled region), and z is a coordinate parallel to the symmetry axis. The electric-field lines are radially oriented, while the magnetic-field lines encircle the symmetry axis. (a) Do some drawing as follows. [7] i. Draw a picture of the waveguide with the symmetry axis directly along your line of sight. ii. Based on your choice of the +z-direction, draw in the electric- and magnetic-field lines at some moment in time in this line-of-sight picture such that the lines are consistent with the way in which the wave propagates. (b) Determine the relationship between the various parameters, namely E0, B0, k, and ω. [4] (c) Determine the instantaneous, as well as the average, power exiting the edge of the waveguide at z = L. [19] (d) Suppose that at the far end of the waveguide, the wave is perfectly absorbed by a sheet of cardboard placed perpendicular to the symmetry axis that caps-off the conducting cylinders. What is the average force exerted by the wave on the absorber? [5]

4. Consider the cylindrical waveguide below, which has an electromagnetic wave propagating in the space between the inner and outer conductors, which is a gap where air exists. The radius of the inner conductor is a, while the inner radius of the outer conductor is b (as shown). The fields in the air-gap have the form Eo E = cos (kz – wt) r Во B= cos (kz - wt) r where Eo and Bo are constants, r is the radial distance from the symmetry axis of the wire (with a <r <b signifying the air-filled region), and z is a coordinate parallel to the symmetry axis. The electric-field lines are radially oriented, while the magnetic-field lines encircle the symmetry axis. (a) Do some drawing as follows. [7] i. Draw a picture of the waveguide with the symmetry axis directly along your line of sight. ii. Based on your choice of the +z-direction, draw in the electric- and magnetic-field lines at some moment in time in this line-of-sight picture such that the lines are consistent with the way in which the wave propagates. (b) Determine the relationship between the various parameters, namely Eo, Bo, k, and w. [4] (e) Determine the instantaneous, as well as the average, power exiting the edge of the waveguide at z = L. (19) (d) Suppose that at the far end of the waveguide, the wave is perfectly absorbed by a sheet of cardboard placed perpendicular to the symmetry axis that caps-off the conducting cylinders. What is the average force exerted by the wave on the absorber? [5]

Answer 1

Here, I have used the concept of waveguide, electric and magnetic field and using required diagram and theories, I have answered the questions.