1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted