# Maxwell's Stress Tensor

1. Jan 22, 2005

### mike217

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

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

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

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

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

Thank you.