(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the electric field from an electric dipole for r>>d is:

[tex]\vec{E} = \frac{Qd}{4\pi\epsilon_0 r^3}(2\cos \theta \hat{r} + \sin \theta \hat{\theta})[/tex]

2. Relevant equations

Electric Field of a Point Charge: [tex]\vec{E}=\frac{Q}{4\pi\epsilon_0r^2}[/tex]

3. The attempt at a solution

First thing first, I can't use Electric potential to solve this, I need to use fields right from the start.

OK, here we go:

[tex]\vec{E}=\vec{E_+}+\vec{E_-}[/tex]

[tex]\vec{E}=\frac{Q}{4\pi\epsilon_0}(\frac{\vec{r_+}}{r_+^3}-\frac{\vec{r_-}}{r_-^3})[/tex]

[tex] \vec{E}=\frac{Q}{4\pi\epsilon_0}(\frac{r_-^3\vec{r_+}-r_+^3\vec{r_-}}{(r_+r_-)^3})[/tex]

Now assume r+ and r- are close to the same length, since r>>d:

[tex]\vec{E}=\frac{Q}{4\pi\epsilon_0r^3}(\vec{r_+}-\vec{r_-})[/tex]

Ok, this is where I get stuck. I know the length of r+ - r- should be dcos(theta) in spherical coordinates, where theta is the angle from the +z axis., but I can't get the unit vector into terms of [tex]\hat{r}[/tex] and [tex]\hat{\theta}[/tex].

Any hints would be appreciated. Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Electric Field of a Dipole Problem

**Physics Forums | Science Articles, Homework Help, Discussion**