Derive energy of electric dipole in electric field

[Jonsson]

Hello there,

I want to derive ##U(\theta) ## for electric dipole placed in uniforum electric field $\vec{E} = E\vec{e}_x$ where E is constant. I define the dipole moment as $p = qd$, where $d$ is the distance from the two

I write $\mathm{d}W = p\,E\sin\theta \mathrm{d}\theta = \tau\mathrm{d}\theta$, but how do I determine what the sign should be? Should it be $\tau\mathrm{d}\theta$ or $-\tau\mathrm{d}\theta$?

I don't understand how to work it out. What determines what the sign should be?

Thank you for your time.

Kind regards,
Marius

 

[mfb]

How did you define theta?
Just consider the energy for different values of theta, that should give the answer.

 

[Jonsson]

Let theta be the angle between ##\vec{p}## and ##\vec{E}##.