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Electrostatic Potential Energy-related.

  1. Mar 26, 2015 #1
    1. The problem statement, all variables and given/known data
    E=(1/4πε0)(Q/r^2) for R<r<2R

    2. Relevant equations
    U= integral (2R,R) ( (ε0 E^2)/2*4πr^2 dr

    3. The attempt at a solution
    I have no idea where the U-formula comes from. Any help would be appreciated.
    I added some pictures so that it could be easier to understand.
    12.jpg 123.jpg
  2. jcsd
  3. Mar 26, 2015 #2


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    Homework Helper
    Gold Member

    Hello Tarabas,

    You might want to look through your textbook in the parts that talk about the energy stored in an electrostatic field. By that I mean the total energy it takes to create a given electrostatic field in the first place.

    To point you in the right direction, the energy density (energy per unit volume) of an electrostatic field is

    [tex] \frac{dU}{dV} = \frac{1}{2} \varepsilon_0 |E|^2 [/tex]

    where [itex] dU [/itex] is the differential potential energy (the potential energy of the space enclosed within the differential volume), [itex] dV [/itex] here refers to the differential volume (where '[itex] V[/itex]' here stands for volume, not to be confused with potential or voltage) and [itex] E [/itex] is the magnitude of the electric field at that point in space. Really though, you should check your textbook because it's likely there are at least a few pages dedicated to this idea.

    Now do you see how the answer you posted in the image is integrating the energy density over the specified volume? :wink: [Edit: which gives you the energy stored in that region of space between [itex] R [/itex] and [itex] 2R [/itex]]
    Last edited: Mar 26, 2015
  4. Mar 27, 2015 #3
    Thanks a lot. I actually checked my textbook and it was nowhere. :D
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