Electric dipole - derive torque from pot. energy

[zimo]

Homework Statement

Derive equation of torque: G = p X E from equation U = -p$\cdot$E

Homework Equations

G = $\int x \times \rho(x)E dV$

U = $\int \rho(x)x \cdot \nabla\varphi dV$

The Attempt at a Solution

I tried to figure how to represent G in a way that better express the nature of the problem. so I figured maybe G = r x F but then got stuck again...

 

[fizika_kz]

Use the relationship between the work and change of the energy.

 

[zimo]

A shot:

$G = - \frac{\partial U}{\partial\theta}<br /> = - \frac{\partial(-p \cdot E)}{\partial\theta}<br /> = \frac{\partial(pEcos\theta)}{\partial\theta}<br /> = - pEsin\theta<br /> = - p \times E$


did I get it all-right?