maxwell stress tensor


by leonne
Tags: maxwell, stress, tensor
leonne
leonne is offline
#1
Apr29-11, 03:55 PM
P: 192
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
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
G01
G01 is offline
#2
Apr30-11, 01:17 PM
HW Helper
G01's Avatar
P: 2,688
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.
leonne
leonne is offline
#3
Apr30-11, 01:24 PM
P: 192
o ok thanks for the info


Register to reply

Related Discussions
Maxwell Stress Tensor Advanced Physics Homework 3
Maxwell Stress Tensor Classical Physics 9
Maxwell Stress Tensor Advanced Physics Homework 0
Maxwell Stress Tensor Advanced Physics Homework 1
Maxwell's Stress Tensor Introductory Physics Homework 0