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

E field of dipoles

  • Thread starter Ghost117
  • Start date
  • #1
50
3
This is part of a question from Griffiths 4.5 (electrodynamics, 4th edition)

Homework Statement



p1 and p2 are (perfect) dipoles a distance r apart (Their alignment is such that p1 is perpendicular to the line separating them (pointing upwards) and p2 is parallel to the line separating them (pointing away from p1).)

What is Field of p1 at p2, and the Field of p2 at p1?

Homework Equations



Edip(r,θ) = p/(4πε0r3) * (2cosθr + sinθθ)

The Attempt at a Solution



I actually have the official solution for this, but I don't understand it... The theta value in the solution uses theta = π/2 for the field of p1 at p2, but a value of theta = π, for the equation for p2 at p1.. And I dont see where either of these theta values are coming from (my spherical coordinates are very weak, and I suspect that's the real problem here.)

Thanks
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
12,528
2,950
Note how θ is defined in the diagram (given back in chapter 3). See attached figure.
Imagine that the dipole shown is p1. Where would p2 be located in this figure? What would be the value of θ at the location of p2?
 

Attachments

  • Like
Likes Ghost117
  • #3
50
3
Note how θ is defined in the diagram (given back in chapter 3). See attached figure.
Imagine that the dipole shown is p1. Where would p2 be located in this figure? What would be the value of θ at the location of p2?
Yes that's the diagram I'm trying to use, and for E1, I can see why theta = pi/2 (since p2 is on the y axis in that diagram, pointing away.) But I don't understand why theta = pi when calculating E2 (field of p2 at p1)... If I set p2 as my zero and count to p1 (clockwise) I get 3pi/2... not pi... I just don't see how I can get pi at all for any angle between these two dipoles...
 
  • #4
blue_leaf77
Science Advisor
Homework Helper
2,629
784
When you want to calculate the field of ##\mathbf{p}_2## at ##\mathbf{p}_1##, you have to use a new coordinate system in which the z axis is parallel to ##\mathbf{p}_2## and its positive direction points in the same direction as ##\mathbf{p}_2## does.
If I set p2 as my zero and count to p1 (clockwise) I get 3pi/2
Polar angle only runs from 0 to ##\pi##.
 
  • Like
Likes Ghost117
  • #5
50
3
When you want to calculate the field of ##\mathbf{p}_2## at ##\mathbf{p}_1##, you have to use a new coordinate system in which the z axis is parallel to ##\mathbf{p}_2## and its positive direction points in the same direction as ##\mathbf{p}_2## does.

Polar angle only runs from 0 to ##\pi##.
Thank you, I suspected it was going to come down to a basic problem with my understanding of the spherical coordinate system.
 

Related Threads on E field of dipoles

  • Last Post
Replies
24
Views
3K
  • Last Post
Replies
0
Views
6K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
8
Views
8K
  • Last Post
Replies
1
Views
1K
Replies
0
Views
2K
Replies
5
Views
17K
  • Last Post
Replies
2
Views
2K
Top