- #1

- 8

- 0

## Homework Statement

Given a uniform plane wave in air as:

E_i=40cos(wt- Bz)a_x +30sin(wt- Bz)a_y

(a) Find H_i

(b) If the wave encounters a perfectly conducting plate normal to the z axis at z = 0, find

the reflected wave E_r and H_r.

(c) What are the total E and H fields for z < 0?

## Homework Equations

[1] direction of H is the cross product of the direction of propagation with the direction of the E wave.

## The Attempt at a Solution

[/B]

This problem should be really easy for me but I'm not getting the boundary conditions I feel like I should have at z=0.

The E wave is propagating in the + z direction with +x and +y components.

Because of equation [1] the corresponding H wave will have corresponding +y and -x components. {Note I don't really care about the magnitude for now}.

Because the wave hits a perfect conducting boundary, the reflection coefficient is -1.

Now the reflected E wave would be propagating in the - z direction with -x and -y components.

From equation [1] the H wave will have corresponding +y and -x components.

Since none of the waves are transmitted and both the E and H are tangential to the boundary at z=0, The sum of the incident and reflective wave of both the E and H wave must be zero, correct? I don't believe there is a surface current or anything like that either.

If you look at the components of the E incident +x , +y and reflected -x , -y the boundary conditions are satisfied at z = 0; Now looking at the H incident +y , -x and reflected +y , -x they are not satisfied.

If there is something dumb I'm doing please let me know, I've spent way too long on this problem.