Force on a charge from an induced dipole

[Yitzach]

Homework Statement

A point charge q is situated a large distance r from a neutral atom of polarizability $$\alpha$$. Find the force of attraction between them.

Homework Equations

$$\vec{E}_{mono}(r)=\frac{q}{4\pi\epsilon_0r^2}\hat{r}$$
$$\vec{E}_{dip}(r,\theta)=\frac{p}{4\pi\epsilon_0r^3}(2\cos\theta\hat{r}+\sin\theta\hat{\theta})$$
$$\vec{p}=\alpha\vec{E}$$

The Attempt at a Solution

$$\vec{E}_{mono}(r)=\frac{q}{4\pi\epsilon_0r^2}\hat{r}$$
$$\vec{p}=\alpha\vec{E}$$
$$\vec{p}=\frac{\alpha q}{4\pi\epsilon_0r^2}\hat{r}$$
$$\vec{E}_{dip}(r,\theta)=\frac{p}{4\pi\epsilon_0r^3}(2\cos\theta\hat{r}+\sin\theta\hat{\theta})$$
$$\vec{E}_{dip}(r,\pi)=\frac{\alpha q}{16\pi^2\epsilon^2_0r^5}(-2\hat{r})$$
$$\vec{E}_{dip}(r,\pi)=-\frac{\alpha q}{8\pi^2\epsilon^2_0r^5}\hat{r}$$
$$\vec{F}=q\vec{E}$$
$$\vec{F}=-\frac{\alpha q^2}{8\pi^2\epsilon^2_0r^5}\hat{r}$$

The result I got was unexpected because that is a repulsive force.
Do I need to go about a longer way or did I mess it up somewhere?

 

[kuruman]

Why do you say that the force is not attractive? It points in the negative $\hat r$ direction, i.e. towards the origin where presumably you put the monopole.