# E field of dipoles

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

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TSny
Homework Helper
Gold Member
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

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• Ghost117
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...

blue_leaf77
Homework Helper
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##.

• Ghost117
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.