1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Manipulation of Electromagnetic fields using curls clarification

  1. Feb 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Question 1. General Plane Waves.
    We may represent a general electromagnetic plane wave by (real part of the complex exponentials)
    [itex]E=E_{0}*e^(i*k*r-iwt) B=B_{0}*e^(i*k*r-iwt)[/itex]

    Show that Faraday's Law becomes iwB0=-ik x Eo
    2. Relevant equations

    dB/dt=- curl of E

    3. The attempt at a solution
    I transformed dB/dt into iwB0e^(ikr-iwt).

    Attempted to perform curl of E on Eoe^(ikr-iwt) but not sure how to work with the r. I thought you might use curl in spherical polars but then you have theta and phi components and I think there's only x, y and z
     
  2. jcsd
  3. Feb 11, 2014 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi gedanken6! :smile:
    just because there's an r, that doesn't mean it stands for "radius"!

    k*r simply means kxi + kyj + kzk :wink:

    (erm … different k)
     
  4. Feb 11, 2014 #3

    vanhees71

    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    No, it's the dot product:
    [tex]\vec{k}\cdot \vec{r}=k_x x+k_y y+k_z z.[/tex]
     
  5. Feb 12, 2014 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    oops! :redface:

    thanks, vanhees71! :smile:
     
  6. Feb 12, 2014 #5

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Start with faraday's law, use Stokes' theorem to produce Maxwell's law for del x E, then just use the given plane wave equations to show the validity of the given relationship between E0 and B0, which is just a matter of some differential calculus.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...