Maxwell stress tensor

  1. 1. The problem statement, all variables and given/known data
    find all elements of maxwell stress tensor for a monochromatic plane wave traveling in z direction and linearly polarized in x.

    2. Relevant equations
    Tij=[tex]\epsilon[/tex]o(EiEj-(1/2)[tex]\delta[/tex]ij E2+1/[tex]\mu[/tex]o(BiBj-(1/2)[tex]\delta[/tex]B2

    3. The attempt at a solution
    So i found what E and B is well not really important to my question but E =Eocos(KZ-wt) X direction
    B=1/c Eocos(KZ-wt)Y direction

    I have the solution, but kind of confused. They only found Txx Tyy Tzz why didnt they find Txy ext or is that wht it means by find all elements, just xx yy zz

    So i found wht Txx is and I got TXX=1/2([tex]\epsilon[/tex]oE2-B21/[tex]\mu[/tex]o they got the same but than that = to zero. Why does it TXX= to zero? Same for Tyy

    thanks
     
  2. jcsd
  3. G01

    G01 2,691
    Homework Helper
    Gold Member

    Your T_xx is correct. As for the off diagonal terms:

    Only one component of E and B are non zero.

    The cross terms in the tensor are all of the form:

    [tex]T_{ij}=\epsilon_0E_iE_j +\frac{1}{\mu_0}B_iB_j[/tex] with i=/=j


    Let's consider the x-y term. That is:

    [tex]T_{12}=T_{xy}=\epsilon_0E_xE_y +\frac{1}{\mu_0}B_xB_y[/tex]

    But, E_y and B_x are zero! Thus, T_xy is zero. Similarly all the other off diagonal elements are zero as well.
     
  4. o ok thanks for the info
     
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