Homework #14
1) 6.3.1 (text)
2) A uniform plane wave propagating in free space is normally incident on
a dielectric half space with a relative permittivity of 9. The planar interface separating the two media is situated in the x = 0
plane. The magnetic field of the incident plane wave is propating in the positive x-direction, and is described as
H = ayHoe-jkx
a) Compute the incident electric field in the region x < 0.
b) Pose solutions to the magnetic field wave equation for the reflected wave in the region x < 0, and the transmitted wave in the region x > 0
c) Compute the reflected and transmitted electric fields from the posed magnetic fields
d) Express the appropriate boundary conditions at the dielectric interface needed to compute the unknown coefficients weighting the reflected and transmitted waves.
e) Using the boundary conditions, compute the reflection and transmission coefficients.
f) Determine the unique expressions for the total electric and magnetic fields in the regions x < 0 and x > 0.
3) A uniform plane wave propagating in free space is normally incident on
a perfectly electrical conducting (PEC) plane, situated in the z = 0 plane.
The electric field of the incident plane wave is propating in the positive z-direction, and is described as
E = axe-jkz
a) Compute the incident magnetic field.
b) Pose solutions for the electric field in the region z < 0 and z > 0.
c) Express the necessary boundary conditions in the z = 0 plane that are sufficient to solve for the reflected electric field.
d) Using the boundary condition(s), compute the total electric field in the region z < 0 and z > 0.
e) Demonstrate that the wave in the region z < 0 is a perfect standing wave.
f) It is found that the electric field is 0 at distances from the PEC
wall of 1 m, 2 m, 3 m, .... Determine the frequency of the incident wave.