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

AI Thread Summary
The discussion centers on calculating the intensity of an electromagnetic wave using the given rms value of the magnetic field, Brms = 0.137 T. The user attempts to derive the electric field and intensity using the equations E = cB and I = (ErmsBrms) / μ0, resulting in an intensity of 4.47 x 10^12 W/m², which does not match the provided answer choices. Participants suggest that the formulas apply to both rms and peak values, and converting Brms to its peak value might be necessary. Ultimately, the calculations confirm that the derived electric field remains consistent regardless of whether rms or peak values are used. The discussion highlights the importance of correctly applying formulas in electromagnetic wave calculations.
KKuff
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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) / \mu0

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\pi 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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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) / \mu0

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\pi 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) / \mu0

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.
 
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 \sqrt{}2 = Bpeak
0.137 T x \sqrt{}2 = 0.194 T

and using E = cB
Epeak = 5.82 x 107

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