1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Plane Wave at Barrier

  1. May 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Sorry for the dull question. Problem is as shown/attached
    Screen Shot 2016-05-28 at 12.10.47.png

    2. Relevant equations
    The waves in part ii) are travelling in a HIL dielectric of permittivity ##\epsilon_{r}## from ##0 <z<d## and then hit an ideal metal boundary at ##z=d##.

    3. The attempt at a solution
    I figure this should be quite obvious! The total field in the dielectric ##\vec{E_{D}}## is the superposition of the reflected and incident waves. At ##z=d## the field parallel to the boundary must be 0 -ideal metal is ideal conductor and so electrons can move to precisely counteract the field. We also know (from applying Faraday's law to a small loop around the boundary) that the parallel electric field must be continuous across the boundary. i.e

    $$ \vec{E_{d}} =E_{D}\hat{\mathbf{x}}= \bigg(E_{xi}exp[i(kz-\omega t)] + E_{xr} exp[i(-kz-\omega t) ]\bigg)\hat{\mathbf{x}} $$
    [n.b - the frequency of the incident and reflected waves has to be the same, else we couldn't satisfy the boundary condition for all t,] So:
    $$ E_{D}(z=d) =0 \implies E_{xi} \big[cos(kd) +isin(kd)\big] =-E_{xr} \big[cos(kd)-isin(kd)\big] $$
    $$ E_{xr} = -\frac{ cos(kd)+isin(kd)}{cos(kd)-isin(kd)} E_{xi} $$
    Which is obviously not the result I'm meant to get! What has gone wrong?
     
  2. jcsd
  3. Jun 1, 2016 #2

    RUber

    User Avatar
    Homework Helper

    It looks to me that the given formula for the plane wave is for free space for z<0. So, you have the first get the expression for the wave inside the dielectric. That is where you will get the ##\epsilon_r## and ##k'## terms.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Plane Wave at Barrier
  1. Plane and barrier (Replies: 1)

Loading...