Question on the derivation of Intensity

In summary, the conversation discusses the derivation of the intensity of an electromagnetic wave, specifically how the equation I = Watts/m^2 becomes I = u c. The textbook uses an example of an electromagnetic wave traveling through a cylinder with changing cross-sectional areas to explain this concept. The equation I = u c represents the energy density and the energy passed through a given surface for a certain time interval. The concept is further clarified by using the definition of intensity.
  • #1
Blastrix91
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0

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?
 
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  • #2
"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.
 
  • #3
Great. Yeah, that was clear. I'm grateful ^^
 

1. What is intensity and how is it related to energy?

Intensity is the amount of energy transmitted per unit area per unit time. It is directly proportional to the energy of a wave, meaning that as the energy of a wave increases, so does its intensity.

2. How is intensity calculated?

Intensity is calculated by dividing the power of a wave by the area through which it is passing. The formula for intensity is I = P/A, where I is intensity, P is power, and A is the area.

3. What is the difference between intensity and amplitude?

Intensity and amplitude are two different measurements of a wave. While intensity is the amount of energy transmitted per unit area, amplitude is the maximum displacement of a wave from its equilibrium position. In other words, amplitude refers to the height or strength of a wave, while intensity refers to the amount of energy it carries.

4. How does distance from the source affect intensity?

As distance from the source increases, intensity decreases. This is because the same amount of energy is spread out over a larger area, resulting in a lower intensity. The relationship between intensity and distance is inverse, meaning that as distance increases, intensity decreases by the square of the distance.

5. How does the medium through which a wave travels affect intensity?

The medium through which a wave travels can affect its intensity by either absorbing or reflecting the energy of the wave. For example, a medium that is more dense or has more particles will absorb more of the wave's energy, resulting in a lower intensity. On the other hand, a medium that is less dense or has fewer particles will reflect more of the wave's energy, resulting in a higher intensity.

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