Sinusoidal electromagnetic wave help

In summary, to calculate the energy carried by a sinusoidal electromagnetic wave passing through an open window with an area of 0.700m2 and an rms electric field of 2.30×10−2V/m during a 30.0s commercial, the intensity needs to be found first using the equation I = E^2 / (2 * μ-naught * speed of light). This value is then used to calculate the power, which is then multiplied by the time to find the energy. However, since the electric field is given in rms value, it needs to be converted to a peak value before performing the calculations.
  • #1
reed2100
49
1

Homework Statement


A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area of 0.700m2 . At the window, the electric field of the wave has an rms value 2.30×10−2V/m .

How much energy does this wave carry through the window during a 30.0s commercial?

2. Homework Equations

Intensity = Power/area -> I=P/A

I = E^2 / (2 * μ-naught * speed of light)

Energy = power * time

The Attempt at a Solution



First find I since I am given all values needed ?

I = [ (2.3 * 10^-2 )^2 ] / [ 2 *4π * 10^-7 * 3 * 10^8 ]

I = 7.01 * 10^-7

Power = Intensity * area
Power = 7.01 * 10^-7 * (.7)
Power = 4.91 * 10^-7

Energy = power * time
Energy = 4.91*10^-7 * (30)
Energy = 1.47 * 10^ -5 Joules

That's incorrect and I'm having trouble figuring out where I went wrong, as I used the same approach for a similar problem and it worked. The difference between problems was that I wasn't given an rms value, instead I was just told the magnitude of the field if I remember correctly. I thought the rms was just root mean square and was just another way of expressing an "average" -ish value. Do I need to use μ instead of μ naught because it's in air and technically not vacuum? That would confuse me as well because I did a problem in this vein that involved high energy waves through flesh to eliminate cancer cells, and μ naught worked fine. I wouldn't think the program would suddenly switch it's expectations of what simplifications to use for the sake of the course level. Any and all help is greatly appreciated.
 
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  • #2
Did you try converting E to a Peak value from an RMS value before doing your energy calculations? The relationship between RMS and Peak for a sinewave is straightforward.
 
  • #3
gneill said:
Did you try converting E to a Peak value from an RMS value before doing your energy calculations? The relationship between RMS and Peak for a sinewave is straightforward.
Ah, that did it. I wasn't aware of the rms to peak necessity, I must have glazed over it in my reading or something. Thank you!
 

Related to Sinusoidal electromagnetic wave help

1. What is a sinusoidal electromagnetic wave?

A sinusoidal electromagnetic wave is a type of electromagnetic radiation that oscillates in a sinusoidal pattern. This means that the electric and magnetic fields of the wave vary in a regular, repeating manner, creating a wavelike pattern. Examples of sinusoidal electromagnetic waves include radio waves, visible light, and X-rays.

2. How is the amplitude of a sinusoidal electromagnetic wave related to its intensity?

The amplitude of a sinusoidal electromagnetic wave is directly proportional to its intensity. This means that as the amplitude increases, the intensity of the wave also increases. Conversely, when the amplitude decreases, the intensity decreases as well.

3. What is the relationship between the frequency and wavelength of a sinusoidal electromagnetic wave?

The frequency and wavelength of a sinusoidal electromagnetic wave are inversely related. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation c = fλ, where c is the speed of light, f is the frequency, and λ is the wavelength.

4. How are sinusoidal electromagnetic waves produced?

Sinusoidal electromagnetic waves are produced when an electric charge is accelerated or decelerated. This can occur naturally, such as in the case of light from the sun, or artificially, such as in the case of radio waves produced by electronic devices.

5. What are some practical applications of sinusoidal electromagnetic waves?

Sinusoidal electromagnetic waves have many practical applications in our daily lives. Radio waves are used for communication, visible light allows us to see, and X-rays are used for medical imaging. They are also used in technologies such as radar, microwave ovens, and wireless internet. In addition, sinusoidal electromagnetic waves play a crucial role in understanding the universe, as they are used in telescopes and other instruments to observe and study celestial objects and phenomena.

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