Field Angular Momentum (Thomson Dipole)

  • Thread starter Septim
  • Start date
  • #1
167
5

Homework Statement


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.

Homework Equations



mu_0*epsilon_0*Poynting Vector = Momentum density

Position vector X Momentum density = Angular momentum density

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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Attachments

  • Attempt_page2.jpg
    Attempt_page2.jpg
    13.8 KB · Views: 522
  • Question.png
    Question.png
    23.5 KB · Views: 537
  • Attempt_page1.jpg
    Attempt_page1.jpg
    15.5 KB · Views: 449

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
13,324
3,600
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:

Related Threads on Field Angular Momentum (Thomson Dipole)

Replies
4
Views
14K
Replies
4
Views
2K
  • Last Post
Replies
2
Views
605
Replies
1
Views
764
Replies
2
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
1K
Top