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Field Angular Momentum (Thomson Dipole)

  1. Dec 26, 2012 #1
    1. The problem statement, all variables and given/known data
    I have attached the question as jpg to this post. Typing these were too time consuming and I uploaded the relevant sections as image files, thanks for your understanding.

    2. Relevant equations

    mu_0*epsilon_0*Poynting Vector = Momentum density

    Position vector X Momentum density = Angular momentum density

    3. The attempt at a solution
    These too are attached in png format.

    I have found out that angular momentum density has two components, one in the z direction and one in the x direction. According to the books solution the x component integrates to zero but I was unable to verify this and I am highly skeptical about this topic. Any help would be appreciated. I have attached the relevant information to this post.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Dec 27, 2012 #2

    TSny

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    Homework Helper
    Gold Member

    In constructing your equation (8), note that ##\hat{r}## will generally have a ##\hat{y}## component as well as ##\hat{x}## and ##\hat{z}## components: ##\hat{r} = (\hat{r} \cdot \hat{x}) \hat{x} + (\hat{r} \cdot \hat{y}) \hat{y} + (\hat{r} \cdot \hat{z}) \hat{z}##.

    ##\hat{r} \cdot \hat{x} = sin\theta cos\phi##, etc.

    See what you get for the x and y components of the angular momentum when you integrate over ##\phi##.
     
    Last edited: Dec 27, 2012
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