# Explanation of E-field torque and initial angle

1. Jan 28, 2014

### jonochar

1. The problem statement, all variables and given/known data
Hello,
A dipole moment is placed in a uniform electric field oriented along an unknown direction. The maximum torque applied to the dipole is equal to 0.1 N.m. When the dipole reaches equilibrium its potential energy is equal to -0.2 J. What was the initial angle between the direction of the dipole moment and the direction of the electric field?

2. Relevant equations
torque = pEsin(theta)
Potential Energy = pEcos(theta)
Work = pEcos(Θ2) - pEcos(Θ1)

3. The attempt at a solution
I got the correct answer, which was about 26.5°. What I am unsure about is why that worked, and how would I have understood that intuitively, I googled the question after attempting it for a while.
To get that answer. The maximum torque was divided by the potential energy, and then the inverse tan was taken to get the angle. I'm not sure what this means and I would appreciate help.

edit: also, it's possible that this may be the wrong answer, I selected 30 degrees (multiple choice) and assumed it may have been rounded, since my teacher likes to round out to easier numbers

Last edited: Jan 28, 2014
2. Jan 28, 2014

### rude man

Potential energy is not pEcos(x) when the dipole is at its minimum energy alignment. That's its potential energy when it's aligned to the original angle x.

That angle is indeed 30 deg.

3. Aug 7, 2015

### luriol

This is a poorly worded problem, which makes it confusing. What they mean is that the dipole is placed in an electric field -> while a torque of 0.1N/m is applied to it <-. Under the influence of the torque it remains at some unknown angle theta. After the torque is released it returns to its equilibrium (lowest energy) state. The potential energy of that state is -0.2 J.

Last edited: Aug 7, 2015