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1. When the dipole moment ##\vec{p}## is in the same direction as the electric field (uniform) it has the least potential energy. To me this makes sense because there is no torque acting on the dipole at that moment and it (probably) has the most kinetic energy at that time, like a pendulum. But then when the direction of the moment is exactly opposite that of the field, we define it to have the greatest potential energy. This doesn't make sense because the dipole is in exactly the same situation as when it is in the same direction as the field - there is no torque acting on it? Why when the moment is perpendicular to the field does it not have the greatest potential energy - that is when the biggest torque is applied.

2. When deriving the expression for potential energy we use U = - W. We have that

##-W = -\int_{90}^{\theta}\tau~d\theta = - -\int_{90}^{\theta}(-pEsin\theta)d\theta##

I don't understand why we add the extra minus sign, because in the actual expression for torque there is no minus sign.

3. I have an idea as to why we start with a lower limit of 90 - we want that orientation to have zero potential energy, but what's really going on here? I don't completely understand it.

4. Another thing is that the least potential energy, when we derive it this way is -pE and the max is +pE. This is apparently the most convenient way to define it. But to fully understand something we should do it in multiple ways. What if I wanted to make it go from 0 to 2pE?

Edit: The uniform field is an electric field