Boundary conditions of a plane wave on a conductor

Tags:
1. Apr 24, 2017

1v1Dota2RightMeow

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. Apr 29, 2017

PF_Help_Bot

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.