1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Relating time averaged energy density to the Poynting vector per unit solid angle

  1. Oct 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Basically, the problem states that a cavity at temperature T is emitting EM waves isotropically in all directions (with frequency distribution of Planck's Law). If the time averaged density is <e>, find the value of d<S>/dw where w is the solid angle and the quantity is the effective poynting vector magnitude per unit solid angle. Hence I am to show the power per unit area that passes in one direction (i.e. into solid angle of 2 pi) through any plane within the cavity is dP/dA= (c/4)<e>/ Note that the unit system is Gaussian. Basically, I am stuck at the first part of the problem.

    2. Relevant equations

    Some equations that I know are <S>=c<e>, the total solid angle for a sphere is 4 pi.

    3. The attempt at a solution

    I have a feeling the solution is really simple but I cannot get into the physics of it. Is d<S>/dw just <S>/ 4pi= (c/4 pi)<e>? But then integrating over a solid angle of 2 pi gives me (c/2)<e> which is off by a factor of 2. And I really don't get the solid angle business. Can someone point me in the right direction? Thanks.
  2. jcsd
  3. Oct 20, 2008 #2
    "But then integrating over a solid angle of 2 pi gives me (c/2)<e> which is off by a factor of 2"

    That's because you should be integrating over a solid angle of 4 pi, as you already know!
  4. Oct 20, 2008 #3
    but now i want the power per unit area passing through one direction and that has a solid angle of 2 pi not 4 pi. the qn requires me to show that integrating over the solid angle of 2 pi gives me (c/4)<e>
  5. Oct 20, 2008 #4
    I did misread your question, sorry about that. In any case, the relation |<\vec{S}>|=c<e> holds for plane waves propagating in a given direction. It's not a general relation.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook