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Show wave equations for E & B consistent with potentials

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data

    There are a couple of introductory questions that aren't relevant to the last parts then it says:

    (d) If the current density is time independent and divergence free, show that the Maxwell Equations separate into independent equations for E and B.

    (e) Express E in terms of the electrostatic potential φ, and B in terms of the vector potential A. Show that the equations in question (d) are satisfied when (in Coulomb Gauge) φ and A satisfy Poisson equations. Write down those equations.

    3. The attempt at a solution

    I have (with some help) figured out (d) and I got a homogeneous wave equation for B and an inhomogeneous wave equation for E (the inhomogeneity created by a ∇(ρ/ε) term).

    However subbing in A and φ for B and E leads only to mess, I have no idea how to simplify it. I looked through a list of identities, but they were no help. I need to find a way to rearrange it so that I can make use of properties like the Coulomb Gauge and Poisson's equation, but I'm not sure how.

    Any help would be great, thanks.
  2. jcsd
  3. Nov 26, 2008 #2


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    Homework Helper
    Gold Member

    If you show me the mess you are getting, I'll be better able to help you.
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