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

  1. Jul 30, 2011 #1
    1. The problem statement, all variables and given/known data
    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...

    2. Relevant equations

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

    3. 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.
     
  2. jcsd
  3. Jul 30, 2011 #2

    PeterO

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    Homework Helper

    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.
     
  4. Jul 30, 2011 #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
     
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