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Deriving wave eqn. from Faraday & A.M.

  1. Apr 22, 2013 #1
    1. The problem statement, all variables and given/known data
    I'm asked to start from Faradays Law & Ampere-Maxwell law then derive the equation for the magnetic field, B, in the form;

    del2B = 1/c2 * d2B/dt2



    2. Relevant equations
    Faraday: curl E = -dB/dt
    A.M : curl B = ε0μ0 dE/dt


    3. The attempt at a solution
    taking curl of both sides of AM

    rhs
    curl curlB = grad div B - del2B
    no monopole says divB = 0
    so = - del2B

    lhs
    curl curl B = ε0μ0 curl dE/dt
    rearrange
    = ε0μ0 d/dt curl E
    Faraday says curl E = -dB/dt

    in the next step of working out I don't get why this goes to
    -ε0μ0 d2B/dt2
    instead of
    -ε0μ0 dB/dt

    Addled, I must be [Yoda]
     

    Attached Files:

    Last edited: Apr 22, 2013
  2. jcsd
  3. Apr 22, 2013 #2
    [itex]-\nabla ^2 \mathbf{B} = \epsilon_0 \mu_0 \frac{\partial}{\partial t}\nabla \times E[/itex]

    Try the substitution for [itex]\nabla \times E[/itex] again.
     
  4. Apr 22, 2013 #3
    Thank you.
    Nose - Face - well known phrase.
     
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