 #1
cwill53
 214
 40
 Homework Statement:

If the source of an electric field is to be a continuous charge distribution, rather than point charges, the following integral gives the electric field at (x,y,z) which is produced by charges at other points (x’,y’,z’):
$$\vec{E}(x,y,z)=\frac{1}{4\pi \varepsilon _{0}}\int \frac{\rho (x',y',z')\hat{r}dx'dy'dz'}{r^{2}}$$
This is a volume integral, letting the variables of integration x’,y’,z’ range over all space containing charge, thus summing up the contributions of all the bits of charge. The unit vector ##\hat{r}## points from (x’,y’,z’) to (x,y,z) unless you put a minus sign in front of the integral which just reverses the direction of ##\hat{r}##.
 Relevant Equations:
 $$\vec{F}=q\vec{E}$$
I sort of understand the meaning of this integral, but I don't know how to evaluate it. I have never evaluated a volume integral. It would be very helpful if someone could explain in other words what this integral means and give an example evaluating it.
This is from Purcell's Electricity and Magnetism, 3rd Edition, by the way.
This is from Purcell's Electricity and Magnetism, 3rd Edition, by the way.