Intensity of an electromagnetic wave, given only rms value of magnetic field

In summary: So it seems like the formulas are consistent, and I still can't figure out why the answer is not one of the choices.In summary, the problem involves finding the intensity of an electromagnetic wave with a given rms value of the magnetic field. The formula for intensity is I = (ErmsBrms) / \mu0, where Brms is the rms value of the magnetic field and Erms is the corresponding rms value of the electric field. The solution involves converting the rms value of the magnetic field to a peak value using Brms x \sqrt{}2, and then using E = cB to find the corresponding peak value of the electric field. Finally, the peak value of the electric field is converted back to an rms
  • #1
KKuff
9
0

Homework Statement


Hi, here is the problem I'm having trouble with:

The rms value of the magnitude of the magnetic field in an electromagnetic wave is Brms = 0.137 T. The intensity of this wave is approximately...

Homework Equations



E = cB
I = (ErmsBrms) / [itex]\mu[/itex]0

The Attempt at a Solution



E = (3 x 108)(0.137 T) = 4.11 x 107 V/m
I = ((4.11 x 107 V/m)(0.137 T)) / (4[itex]\pi[/itex] x 10-7) = 4.47 x 1012 W/m2

I keep re-doing this problem and I keep coming up with that same answer, but it is not one of the answer choices. Can anyone give me a clue as to what I'm doing wrong? Thanks, I appreciate it.
 
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  • #2
KKuff said:

Homework Statement


Hi, here is the problem I'm having trouble with:

The rms value of the magnitude of the magnetic field in an electromagnetic wave is Brms = 0.137 T. The intensity of this wave is approximately...

Homework Equations



E = cB
I = (ErmsBrms) / [itex]\mu[/itex]0

The Attempt at a Solution



E = (3 x 108)(0.137 T) = 4.11 x 107 V/m
I = ((4.11 x 107 V/m)(0.137 T)) / (4[itex]\pi[/itex] x 10-7) = 4.47 x 1012 W/m2

I keep re-doing this problem and I keep coming up with that same answer, but it is not one of the answer choices. Can anyone give me a clue as to what I'm doing wrong? Thanks, I appreciate it.

The second formula you are using:

I = (ErmsBrms) / [itex]\mu[/itex]0

specifically refers to Brms while the first

E = cB

Just refers to B.

Does that mean you should change the RMS value into some other type of value before substituting?

Not claiming that is correct, just a thought.
 
  • #3
Thanks for the reply.
I believe that that formula works both for rms values and peak values.

This should give me the rms value of the electric field
E = (3 x 108)(0.137 T) = 4.11 x 107 V/m

If I convert the magnetic field rms value to peak I would get
Brms x [itex]\sqrt{}2[/itex] = Bpeak
0.137 T x [itex]\sqrt{}2[/itex] = 0.194 T

and using E = cB
Epeak = 5.82 x 107

and converting to rms
(5.82 x 107) / [itex]\sqrt{}2[/itex] = 4.11 x 107 V/m
 

1. What is the relationship between the intensity of an electromagnetic wave and the rms value of the magnetic field?

The intensity of an electromagnetic wave is directly proportional to the square of the rms value of the magnetic field. This means that as the rms value of the magnetic field increases, the intensity of the electromagnetic wave also increases.

2. How is the intensity of an electromagnetic wave affected by changes in the rms value of the magnetic field?

Any changes in the rms value of the magnetic field will directly affect the intensity of the electromagnetic wave. An increase in the rms value will result in a higher intensity, while a decrease in the rms value will result in a lower intensity.

3. Can the intensity of an electromagnetic wave be determined solely by the rms value of the magnetic field?

No, the intensity of an electromagnetic wave cannot be determined solely by the rms value of the magnetic field. Other factors, such as the frequency and wavelength of the wave, also play a role in determining the intensity.

4. How does the intensity of an electromagnetic wave change as it travels through different mediums?

The intensity of an electromagnetic wave can change as it travels through different mediums due to factors such as absorption, reflection, and refraction. These changes can affect the rms value of the magnetic field and therefore impact the overall intensity of the wave.

5. Is the intensity of an electromagnetic wave affected by the direction of the magnetic field?

Yes, the intensity of an electromagnetic wave can be affected by the direction of the magnetic field. This is because the intensity is directly proportional to the square of the rms value of the magnetic field, which can change depending on the direction of the field.

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