Finding intensity from the Poynting vector

4 replies · 2K views · last reply
OhNoYaDidn't
Messages
25
Reaction score
0

Homework Statement


Handwritten problem: plane electromagnetic wave E = x̂ E0 cos(wt - Kz), asking to show the power per unit time irradiating a box a x b x d, with the result P(t) = (1/2) sqrt(e0/mu0) E0^2 a b [cos 2wt - cos 2(wt - Kd)].
[/B]

Homework Equations



The Attempt at a Solution


I found the expression for the magnetic field, and then the Poynting vector.
Handwritten derivation of a plane electromagnetic wave: E = x̂ E0 cos(kz - ωt), B = (1/c) k̂ × E giving B = (1/c) E0 cos(kz - ωt) ŷ, a note that the wave travels in the +z direction, and S = (1/μ0) E × B = (1/(cμ0)) E0² cos²(kz - ωt) ẑ.


If i find the intensity, that's the same as finding the average value of the Poynting vector, and the cos^2 disappears... Can you tell me what to do next?
Thank you.
 
Bump Bump. Does anyone know what to do next?
 
OhNoYaDidn't said:
Bump Bump. Does anyone know what to do next?
Please observe the Forum Rule regarding bumping.

Bumping
Do not "bump" one of your threads to the top of a forum's thread list by posting a basically empty message to it, until at least 24 hours have passed since the latest post in the thread; and then do it only once per thread.​
 
OhNoYaDidn't said:

Homework Statement


Handwritten problem: plane electromagnetic wave E = x̂ E0 cos(wt - Kz); show the power irradiating a rectangular box axbxd, parallel to the axis, is P(t) = (1/2) sqrt(ε0/μ0) E0² a b [cos 2wt - cos 2(wt - Kd)].
[/B]

Homework Equations



The Attempt at a Solution


I found the expression for the magnetic field, and then the Poynting vector.
Handwritten derivation of a plane electromagnetic wave: E = x̂ E0 cos(kz - ωt), B = (1/c) k̂ × E giving B = (1/c) E0 cos(kz - ωt) ŷ, the wave traveling in the +z direction, and S = (1/μ0) E × B = (1/(cμ0)) E0² cos²(kz - ωt) ẑ.


If i find the intensity, that's the same as finding the average value of the Poynting vector, and the cos^2 disappears... Can you tell me what to do next?
Thank you.
What does the Poynting vector tell you about the wave's intensity? What are it's units?

How is the speed of light, c, related to ε0 and μ0 ?
 
I wasn't aware of that rule, thank you for pointing it out.
The intensity is the mean value of the Poynting vector. The units of the Poynting vector are W.m^-2, the same for intensity..
I can use the retation c=1/sqrt(ε0*μ0), and therefore reducing 1/cε0 = sqrt(ε0/μ0). What should i do next?

Thanks for your reply.