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Gauge conditions concerning vector potential and potential

  1. Jul 4, 2013 #1
    Hi everyone

    1. The problem statement, all variables and given/known data

    Give is a generall gauge transformation [tex] \Phi \rightarrow \Phi ' =\Phi -\frac {\partial \chi}{\partial t}[/tex]
    and
    [tex]\vec A \rightarrow \vec A' = \vec A + \nabla \chi[/tex]

    first task for now is the following: How do I have to choose Chi in order to fulfill the lorenz gauge condition.
    2. Relevant equations
    [tex] {\rm div} \vec A + \frac{1}{c^2} \frac{\partial}{\partial t}\phi = 0[/tex]


    3. The attempt at a solution
    FIrst of all I'm not even sure if I have to discuss phi and A as if they are linked to each other or not. But let's take a look at my A

    I tried to use the divergence on my A'

    [tex]div \vec A' = div \vec A + div \nabla \chi[/tex] then I use the Lorenz gauge condition for div a and I finally get

    [tex] \nabla ^2 \chi +\mu_0 \epsilon_0 \frac {\partial^2 \chi}{\partial t^2}=0[/tex]

    Is this the right approach ? I'm stuck here though I don't know how I have to choose my chi now and I still haven't taken a look at my potential.

    Thanks for your help in advance.
     
  2. jcsd
  3. Jul 4, 2013 #2

    dextercioby

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    Homework Helper

    That's correct. Lorenz gauge implies that the parameter is a solution of the free wave equation.
     
  4. Jul 4, 2013 #3
    thanks for the quick reply. Do I have to do something else with my potential phi or is the task done with that?
     
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