Maxwell's Stress Tensor

  1. Consider an infinite parallel plate capacitor with the lower plate (at z=-d/2) carrying the charge density[tex]- \sigma [/tex] and the upper plate (at z=d/2) carrying the charge density [tex]\sigma[/tex].

    Determine all nine elements of the stress tensor in the region between the plates. Display your answer as a 3x3 matrix.

    [tex]\left(\begin{array}{cc}Txx&Txy&Txz\\Tyx&Tyy&Tyz\\Tzx&Tzy&Tzz\end{array}\right)[/tex]

    To calculate the matrix I must calculate [tex] Tij = \epsilon(EiEj-0.5\delta ij E^2)+1/\mu (BiBj-0.5\delta ij B^2)[/tex]

    By calculating the E-field between the plates I get [tex]\sigma / \epsilon\ z[/tex]. My question is how do I calculate the other EiEj and BiBj components.

    Thank you.
     
  2. jcsd
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