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!

Boundary conditions of a plane wave on a conductor

  1. Apr 24, 2017 #1
    1. The problem statement, all variables and given/known data
    Consider a plane monochromatic wave incident on a flat conducting surface. The incidence angle is ##θ##. The wave is polarized perpendicular to the plane of incidence. Find the radiation pressure (time-averaged force per unit area) exerted on the surface.

    2. Relevant equations
    Radiation pressure for reflection ##\to ####P_{reflected} = \frac{2\langle S \rangle \cos ^2 (\theta_I)}{c}##

    ## \vec{S} = \frac{1}{\mu_0}(\vec{E} \times \vec{B})##

    ##\vec{E} = E_0 e^{i(\vec{k} \cdot \vec{r} - wt)}\hat y##

    ##\vec{B} = \frac{1}{v_1}E_0 e^{i(\vec{k} \cdot \vec{r} - wt)}(-\cos \theta_I \hat x + \sin \theta_I \hat z)##

    3. The attempt at a solution
    ##\vec{E} \times \vec{B} = \frac{1}{v_1}E_0^2 e^{2i(\vec{k} \cdot \vec{r} - wt)}(\sin \theta_I \hat x + \cos \theta \hat z)##

    ##\vec{k} \cdot \vec{r} = zk \sin \theta_I + xk \cos \theta_I##

    ##\to P = \frac{2}{\mu_0 c^2}E_0^2 e^{2i((zk \sin \theta_I + xk \cos \theta_I) - wt)}(\sin \theta_I \hat x + \cos \theta_I \hat z)##

    But I know this isn't right because I need to find the time average of the Ponyting vector. How do I do so?
     
  2. jcsd
  3. Apr 29, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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: Boundary conditions of a plane wave on a conductor
Loading...