Understanding of Maxwell's Stress Tensor

[vwishndaetr]

Was a bit fuzzy as to whether this better fit HW or here, but since there really is no question associated with it, figured this made a bit more sense.

I have a couple basic questions about the stress tensor:

$$T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) + \frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} \delta_{ij} B^2 \right)$$

For the component electric and magnetic fields (denoted with "i" and "j" indices), they are what they are. What ever the indice at the time, that particular component fills it in. But for both the squared Electric and Magnetic Field terms, what is being squared? Is it the magnitude of the net field squared?

Might be a bit silly to be dealing with Tensors and asking such silly questions, but still want to know.

Thanks.

 

[Born2bwire]

It implicitly means the dot product of the vector field with itself.

$$E^2 = \mathbf{E}\cdot\mathbf{E}$$

 

[vwishndaetr]

It implicitly means the dot product of the vector field with itself.

$$E^2 = \mathbf{E}\cdot\mathbf{E}$$

So it'd be,

$${E^2} = \sqrt {{E_x}^2 + {E_y}^2 + {E_z}^2} \cdot \sqrt {{E_x}^2 + {E_y}^2 + {E_z}^2}$$

I feel so dumb asking this. Thanks again.

 

[Born2bwire]

So it'd be,

$${E^2} = \sqrt {{E_x}^2 + {E_y}^2 + {E_z}^2} \cdot \sqrt {{E_x}^2 + {E_y}^2 + {E_z}^2}$$

I feel so dumb asking this. Thanks again.

Or more simply just

$${E^2} = {E_x}^2 + {E_y}^2 + {E_z}^2$$