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Field Angular Momentum (Thomson Dipole) 
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#1
Dec2612, 11:29 AM

P: 121

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 


#2
Dec2712, 01:06 PM

HW Helper
Thanks
P: 4,847

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##. 


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