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: Convert tensor from cartesian to cylindrical coordinate

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Given the tensor
    [tex]
    F_{\mu \nu }=
    \left[ \begin{array}{cccc} 0 & -E_{x} & -E_{y} & -E_{z} \\ E_{x} & 0 & B_{z} &-B_{y} \\E_{y} & -B_{z} & 0 & B_{x} \\E_{z} & B_{y} & -B_{x} & 0 \end{array} \right]
    [/tex]
    [tex]
    F^{\mu \nu }F_{\mu \nu }=2(B^2-\frac{E^2}{c^2})
    [/tex]
    and metric tensor
    [tex]
    n_{\mu \nu }=
    \left[ \begin{array}{cccc}c^2& 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -r^2 & 0 \\ 0 & 0 & 0 & -1 \end{array} \right]
    [/tex]

    How to convert it into cylindrical coordinates, that is in terms of Eθ,Ez,Er
    More info of this tensor can be viewed at http://en.wikipedia.org/wiki/Electromagnetic_tensor


    2. Relevant equations



    3. The attempt at a solution

    I try to convert it using the transformation matrix and tensor transformation rule but it turns out that
    [tex]
    F^{\mu \nu }F_{\mu \nu }≠2(B^2-\frac{E^2}{c^2})
    [/tex]

    Can anyone give me some idea how to solve this?
    Thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 18, 2012 #2
    No one can help?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook