1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Application of Dirac delta

  1. Nov 21, 2011 #1
    1. The problem statement, all variables and given/known data
    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]


    2. Relevant 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]

    3. 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!
     
  2. jcsd
  3. Nov 21, 2011 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You're right. There's zero net charge. A zero net charge doesn't necessarily mean the dipole and quadrupole moments vanish, however.
     
  4. Nov 21, 2011 #3
    That's a relief. I still find the delta function a bit confusing.

    ahh, I hadn't realised that about the moments. so I worked out the dipole moment like this:

    [itex]\vec{P} = \int \rho(\vec{r}) \vec{r} \delta(\vec{r} - R\vec{e_{x}}) d^{3} = \Sigma q_{i}\vec{r}_{i}[/itex]

    which in this case was also zero due to cancelling. I'm guessing the quadrupole moment is non-zero, which will be fun :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Application of Dirac delta
  1. Dirac delta (Replies: 5)

  2. Delta dirac (Replies: 6)

  3. Delta dirac integral (Replies: 2)

Loading...