# Calculating E Field of Dipoles at Distance r: Griffiths 4.5 Solution

• Ghost117
In summary: I really appreciate your help!In summary, the calculation of the field of p1 at p2 and the field of p2 at p1 involves using a new coordinate system in which the z axis is parallel to p2 and its positive direction points in the same direction as p2 does. This results in a different value for the polar angle, with theta = pi/2 for p1 at p2 and theta = pi for p2 at p1. This is due to the definition of theta in the given diagram and the need to use a new coordinate system for the calculations.
Ghost117
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 don't 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

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

• dipole coordinates.png
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Ghost117
TSny said:
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...

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.
Ghost117 said:
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
blue_leaf77 said:
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.

## 1. How do I calculate the electric field of dipoles at a distance r?

In order to calculate the electric field of dipoles at a distance r, you can use the formula provided in Griffiths 4.5 Solution. This formula involves the dipole moment, the distance r, and the angle between the dipole moment and the direction of the electric field.

## 2. What are the units of the electric field in this calculation?

The units of the electric field in this calculation are typically given in volts per meter (V/m).

## 3. Is there a simplified formula for calculating the electric field of dipoles?

Yes, there is a simplified formula for calculating the electric field of dipoles at a distance r. This formula is known as the Coulomb's Law for dipoles and only involves the magnitude of the dipole moment and the distance r.

## 4. Can I use this formula for calculating the electric field of any type of dipole?

Yes, this formula can be used for calculating the electric field of any type of dipole, as long as the dipole moment and distance r are known. This includes electric dipoles, magnetic dipoles, and even molecular dipoles.

## 5. Are there any other factors that can affect the accuracy of this calculation?

Yes, there are a few other factors that can affect the accuracy of this calculation. These include the size and shape of the dipoles, the presence of other nearby charges or dipoles, and the dielectric properties of the surrounding medium.

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