Interaction force, two dipoles

[mathman44]

Homework Statement

A dipole p is directed in the positive z direction at the origin.

The force on a dipole p in an electric field E is $$F=(p\cdot\nabla)E$$

If a second dipole is placed at (r, $$\theta$$), by what factor must r increase – in terms
of p, $$\theta$$ and r – so that the net force between the two dipoles decreases by a factor of 64?

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I don't know how to start this... any hints please? This isn't homework, just a practice test question.

 

[gabbagabbahey]

Homework Statement

A dipole p is directed in the positive z direction at the origin.

The force on a dipole p in an electric field E is $$F=(p\cdot\nabla)E$$

If a second dipole is placed at (r, $$\theta$$), by what factor must r increase – in terms
of p, $$\theta$$ and r – so that the net force between the two dipoles decreases by a factor of 64?

---

I don't know how to start this... any hints please? This isn't homework, just a practice test question.

Well, you have a situation where one dipole is exerting a force on another...you already know how to determine the force exerted on a dipole from an external electric field, so...what is the electric field of a dipole? What force does that field exert on a dipole a distance $r$ away from it (do not assume that the dipoles are aligned)?

 

[mathman44]

The electric field of a dipole is

$$E=\frac{p}{4\pi\epsilon{r^3}}(2cos\theta\hat{\theta}+sin\theta\hat{r})$$

If I break p apart into $$p_r$$ and $$p_\theta$$, dot it with del, then multiply by E, I get a mess of an answer.

 

[mathman44]

This is what I got, by the way:

$$F_(r,\theta)=-3\frac{cos\theta}{4\pi\epsilon{r^4}}(2p_\theta+p_r)$$

Any help please?