<img src="./images/dipole_setup.png" align="left" style="width: 300px";/> Two charges are positioned as shown to the left. The relative position vector between them is $\mathbf{d}$. What is the dipole moment of this configuration? $$\sum_i q_i \mathbf{r}_i$$ 1. $+q\mathbf{d}$ 2. $-q\mathbf{d}$ 3. Zero 4. None of these; it's more complicated than before! Note: * CORRECT ANSWER: A

For a dipole at the origin pointing in the z-direction, we have derived: $$\mathbf{E}_{dip}(\mathbf{r}) = \dfrac{p}{4 \pi \varepsilon_0 r^3}\left(2 \cos \theta\;\hat{\mathbf{r}} + \sin \theta\;\hat{\mathbf{\theta}}\right)$$ <img src="./images/small_dipole.png" align="right" style="width: 200px";/> For the dipole $\mathbf{p} = q\mathbf{d}$ shown, what does the formula predict for the direction of $\mathbf{E}(\mathbf{r}=0)$? 1. Down 2. Up 3. Some other direction 4. The formula doesn't apply Note: * CORRECT ANSWER: D * The formula works far from the dipole only.

### Ideal vs. Real dipole <img src="./images/dipole_animation.gif" align="center" style="width: 450px";/>