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!

Inversion of curl of A formula

  1. Jan 5, 2012 #1
    Hello! I'm reading up on Hamiltonian mechanics and i stumbled on the fact that the curl of the vector potential can be expressed as

    [tex]B_k = \sum_k \epsilon_{kij}\frac{\partial A_i}{\partial x_j}[/tex]

    Now the text that I'm reading says that this formula can be inverted as

    [tex] \sum_k \epsilon_{kij} B_k = \frac{\partial A_j}{\partial x_i} - \frac{\partial A_i}{\partial x_j}[/tex]

    But I then wondered how this inversion would be accomplished?

    I suspect the formula [tex]\sum_k \epsilon_{kij} \epsilon_{klm}= \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl}[/tex] to be involved.
     
  2. jcsd
  3. Jan 5, 2012 #2
    Just substitute the third formula into the first and you get the second.
    What is the problem here?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inversion of curl of A formula
  1. Speaking of curl (Replies: 2)

  2. Curl reversibility? (Replies: 16)

  3. Divergence of curl (Replies: 11)

Loading...