• Support PF! Buy your school textbooks, materials and every day products Here!

Griffith's 3.33

  • Thread starter raddian
  • Start date
  • #1
66
0
I am "continuing this thread" in hopes of asking questions that deal with the meaning of the question. https://www.physicsforums.com/threads/griffiths-e-m-3-33-write-e-field-of-dipole-moment-in-coordinate-free-form.359973/
1. Homework Statement

Show that the electric field of a "pure" dipole can be written in the coordinate-free form
$$E_{dip}(r)=\frac{1}{4\pi\epsilon_0}\frac{1}{r^3}[3(\vec p\cdot \hat r)\hat r-\vec p].$$

Homework Equations


$$E_{dip}(r)=\frac{p}{4\pi\epsilon_0r^3}(2\cos \hat r+\sin\theta \hat \theta)$$

The Attempt at a Solution


I am trying to understand what "coordinate free" means. If the answer is in terms of r hat and theta hat, doesnt that contradict "coordinate free"? AND i would get $$ p = pcos(\theta) \hat r - psin(\theta) \hat \theta $$. Why doesn't p depend on PHI? If it's coordinate free why are we restricting our coordinates to r and theta??
 
Last edited:

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
2,629
784
"Coordinate free" means you don't need to define the coordinate system to write your equation. ##\hat{r}## is a unit vector from the center of the dipole to the observation point, so given the orientation of ##\mathbf{p}## in space, the relative direction of ##\hat{r}## with respect to ##\mathbf{p}## will automatically follow.
 

Related Threads for: Griffith's 3.33

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
3
Views
2K
Top