Electric dipole - derive torque from pot. energy

1. Jul 2, 2011

zimo

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

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

3. 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...

2. Jul 3, 2011

fizika_kz

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

3. Jul 3, 2011

zimo

A shot:

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

did I get it all-right?