Question on the derivation of Intensity

[Blastrix91]

Homework Statement

When deriving the intensity of an electromagnetic wave in my textbook, there was a part I didn't quite get.

It's how I = Watts/m^2 becomes I= u c

My textbook gave an example of a electromagnetic wave through a cylinder, with cross-section area A. In 1 second it would have traveled length c. Now that makes sense.

It then proceed with changing the cross-section area with 1 and by that derives I= u c.. ? I don't get it.

Homework Equations

I = Watts/m^2
I= u c

The Attempt at a Solution

So can anybody help me conceptualise this derivation?

 

[cosmic dust]

"u" is energy density, right? So, for a given volume ΔV you can find the energy content of it, using the relation ΔE = u ΔV. Ok, so far?

If yes, then consider a given surface ΔA and try to find the energy passed through it for some time interval Δt. That amount of energy, after leaving the surface, wouldn't be accumulated in a volume ΔV = ΔA (c Δt)?

If the above makes sence, then use the definition of intensity (I = ΔE/(ΔA Δt) to get the desired result.

 

[Blastrix91]

Great. Yeah, that was clear. I'm grateful ^^