# Homework Help: Energy density (electrodynamics/ Dirac delta etc)

1. Nov 2, 2011

### sunrah

So I have the following velocity vector of a charged particle in an EM field

$\dot{\vec{r}} = (v_{0x}cos(\alpha t) - v_{0z}sin(\alpha t), \frac{qEt}{m} + v_{0y}, v_{0z}cos(\alpha t) + v_{0x}sin(\alpha t))$

and I have to state the energy density, which is defined as follows:

$\tau = \sum \frac{m_{i}}{2}\dot{\vec{r_{i}}}^{2}\delta(\vec{r}-\vec{r}_{i})$

My question is whether all I have to do is substitute the vector in the definition of the energy density or if I have to do something with the Dirac distribution as well. Thanks