- #1

- 198

- 22

## Homework Statement

We have to give the total charge, dipol and quadrupol moments of a charge constellation, but I seem to be falling at the first hurdle.

[itex]Q = \frac{1}{4\pi \epsilon_{0}} \int_{vol} \rho(\vec{r}) d^{3}\vec{r}[/itex]

whereby the charge density of the group of particles is:

[itex]\rho(\vec{r}) =q\delta(\vec{r} - R\vec{e_{x}}) + q\delta(\vec{r} + R\vec{e_{x}}) + q\delta(\vec{r} - R\vec{e_{y}}) + q\delta(\vec{r} + R\vec{e_{y}}) - 2q\delta(\vec{r} - R\vec{e_{z}}) - 2q\delta(\vec{r} + R\vec{e_{z}})[/itex]

## Homework Equations

I'm using the following property of the delta function:

[itex] \int_{vol} \delta(\vec{r} - R\vec{e_{x}}) d^{3}\vec{r} = \int_{vol} \delta(x - R) dx \int_{vol} \delta(y)dy \int_{vol} \delta(z)dz = 1 [/itex]

## The Attempt at a Solution

ok, so I got zero net charge. Which means I don't have a dipol or quadrupol moment either. help!