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Work & Energy (+ve or -ve)?

  • Thread starter jegues
  • Start date
  • #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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Answers and Replies

  • #2
1,097
2
Bump, still looking for some help on this, tests tomorrow!
 

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