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: 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]
    [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


    User Avatar
    Science Advisor
    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted