 #1
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Homework Statement
There are two problems attached that illustrate my confusions, but my questions is more general than this specific example.
Homework Equations
The Attempt at a Solution
For the first problem where we are asked for the potential energy,
When the dipole moment is parallel to the electric field, it has 0 potential energy.
[tex]U_{i} =  \vec{p} \cdot \vec{E} = 0[/tex]
When the dipole rotates 60 degrees, the potential energy is not 0.
[tex]U_{f} = \vec{p} \cdot \vec{E} = pEcos\theta[/tex]
The potential enegry given from the formula is negative, but there are only positive answers as possibilities.
I know it is obvious to choose the positive one that corresponds to our answer, but sometimes both negative a positive quantities are listed as possible answers, and I am often confused on which one to choose.
Why is that negative sign in our formula for potential energy, what's its purpose?
For problem number 2 where we are asked for the work,
Initially there is 0 potential energy in the system (perpendicular),
[tex]U_{i} = 0[/tex]
but then the dipole rotates such that it is parallel to the direction of the field so,
[tex]U_{f} = pE[/tex]
Now,
[tex]W = \Delta U = U_{f}  U_{i} = pE  0 = pE[/tex]
It seems as though the work is negative, but the correct answer is that it is positive.
What am I mixing up?
What do I need to think about and be consistent with to eliminate these sign errors?
Please be as clear as possible. A good example to remember how to determine the sign would be excellent.
Thanks again!
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