Force on a dipole from a point charge?

[warfreak131]

Homework Statement

A point charge q is situated at the origin. A dipole p is placed at r. The angle θ is defined by $\hat{p}\cdot\hat{r}=cos(\theta)$

Calculate the vector force Fp acting on the dipole by the nonuniform E field of the point charge.

Homework Equations

The Attempt at a Solution

I know that the E field of a point charge is 1/4pi e0 * q/r², and that $F=(p\cdot\nabla)E=\nabla E\cdot p$

So since the E field of the point charge doesn't rely on phi or theta, i can just say that $\nabla E=\frac{dE}{dr}\hat{r}=\frac{-q}{2\pi\epsilon_{0}r^{3}}\hat{r}$

Now if I dot that result with p, only the radial portions will remain since $E_{\theta}=E_{\phi}=0$

All that remains is $\frac{-qp_{r}}{2\pi\epsilon_{0}r^{3}}$

 

[Spinnor]

Won't the dipole tend to do react to charge q in the following ways. It will align with the electric field of the charge q ( let q be positive for this example) such that the negative end of the dipole is closest to q, there is a torque on the dipole which depends on the angle between the vectors r and p.

Once the dipole aligns the negative end of the dipole is slightly closer to the positive charge then the positive end of the dipole so this will result in a slight attractive force.

Part of your answer should have a theta dependance?