Maxwell Stress Tensor: Find Elements for Plane Wave in Z Direction

[leonne]

Homework Statement

find all elements of maxwell stress tensor for a monochromatic plane wave traveling in z direction and linearly polarized in x.

Homework Equations

Tij=$$\epsilon$$o(EiEj-(1/2)$$\delta$$ij E²+1/$$\mu$$o(BiBj-(1/2)$$\delta$$B²

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($$\epsilon$$oE²-B²1/$$\mu$$o they got the same but than that = to zero. Why does it TXX= to zero? Same for Tyy

thanks

 

[G01]

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:

$$T_{ij}=\epsilon_0E_iE_j +\frac{1}{\mu_0}B_iB_j$$ with i=/=jLet's consider the x-y term. That is:

$$T_{12}=T_{xy}=\epsilon_0E_xE_y +\frac{1}{\mu_0}B_xB_y$$

But, E_y and B_x are zero! Thus, T_xy is zero. Similarly all the other off diagonal elements are zero as well.

 

[leonne]

o ok thanks for the info