How is potential energy is derived from work here?

  • Thread starter kiwibird4
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  • #1
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Since capacitors can store electrical energy in the form of a electrostatic field between its plates, one can derive that potential energy by looking at the work it takes to "push" the charges around to create the voltage.

Therefore Work =
integral from 0 to Q of V(q) dq =
integral from 0 to Q of (1/C)q dq =
Q^2/2C =
1/2 CV^2=
1/2 VQ which consequently equals the potential energy stored in the capacitor

so my question overall is::
Why it is not negative 1/2 VQ for PE since PE is the negative of work?
Everywhere I look there is never a -PE=W but they immediately equate the two being PE=W. I think I am missing something very simple here.
 

Answers and Replies

  • #2
QuantumQuest
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The whole thing in this case, is the reference point you take. This can either be you (or whatever produces work for that matter) and system ( the capacitor in this case). You must be consistent with what you choose and use in order to derive the appropriate signs.
 

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