How is potential energy is derived from work here?

In summary, the conversation discusses the relationship between capacitors, potential energy, and work. It explains how the potential energy stored in a capacitor can be derived by looking at the work required to create the voltage, and how this can be calculated using the equation 1/2 CV^2. The question posed is why this equation does not include a negative sign, as potential energy is typically represented as -PE. The answer lies in the choice of reference point, which must be consistent in order to derive the correct signs.
  • #1
kiwibird4
8
0
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.
 
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  • #2
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.
 

Related to How is potential energy is derived from work here?

1. What is potential energy and how is it related to work?

Potential energy is the energy that an object has due to its position or state. It is related to work because work is the transfer of energy from one form to another, and potential energy is one of the forms that work can be transformed into.

2. Can potential energy be created or destroyed?

No, according to the law of conservation of energy, energy cannot be created or destroyed, it can only be transferred from one form to another. So, potential energy cannot be created or destroyed, it can only be derived from work done on an object.

3. How is potential energy derived from work?

Potential energy is derived from work when an external force acts on an object and causes it to move against a force of resistance. This work done on the object increases its potential energy, which can then be released or used to do work in the future.

4. What are some examples of potential energy being derived from work?

One example is a person lifting a weight. The work done by the person in lifting the weight increases the potential energy of the weight. Another example is a compressed spring, where work is done in compressing the spring, increasing its potential energy. A stretched rubber band is also an example, where work is done in stretching the band, increasing its potential energy.

5. How is potential energy related to the concept of energy conservation?

Potential energy is related to the concept of energy conservation because it is a form of energy that can be converted into other forms of energy, such as kinetic energy or thermal energy. The total energy of a system, including potential energy, remains constant according to the law of conservation of energy.

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