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Homework Help: Superposition if time varying electric vectors

  1. Mar 25, 2008 #1
    1. The problem statement, all variables and given/known data


    two electric field vectors- E1= E0 cos (kz-wt) i(carat) and E2=E0 cos (kz+wt) i(carat) . what is the magnetic field vector corresponding to the the superposition of these 2 waves?



    2. Relevant equations



    3. The attempt at a solution

    E=E1 + E2 = E0 [2cos{( kz-wt+kz+wt)/2}cos{(kz-wt-kz-wt)/2}]]
    =E0[2coskz][cos wt]
    here the new max amplitude is Emax=E0(2 coskz )
    is this right?? this is a standing wave. then B0= Emax/c= E0(2coskz)/c
    and the final equation for the magnetic field vector will be - B=B0(cos wt) because B and E are in phase in an em wave.
     
  2. jcsd
  3. Mar 25, 2008 #2

    pam

    User Avatar

    Find B for each traveling wave E1 and E2 separately by [tex]B\sim{\hat k}\times E[/tex],
    being careful about the direction of [tex]\hat k[/tex].
    Then add B1 and B2.
     
    Last edited: Mar 25, 2008
  4. Mar 26, 2008 #3
    Hey thanks but can't i do it the way i did it???
     
  5. Mar 26, 2008 #4

    clem

    User Avatar
    Science Advisor

    No. You need to use the curl E Maxwell equation to get B from E.
    That is easy for the traveling waves, but would require taking Curl E for your method.
     
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