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Homework Help: Magnitude of electric field between two concentric oppositely charged

  1. Mar 5, 2014 #1
    1. The problem statement, all variables and given/known data

    Magnitude of electric field between two concentric oppositely charged spheres.


    2. Relevant equations

    3. The attempt at a solution

    So I first went with the simple electric field equation E=V/d

    So I have the potential difference V between the two sphere surfaces. I can't do Latex but hyperphysics has it anyway:


    So I know V.
    And surely, in E=V/d, the distance d is simply b-a.

    So finally I sub my V and d into the equation and I'm left with:

    E = Q/(4πεab)

    Which looks reasonable enough.. But all sources on the Internet tell me that the answer is simply:


    The real confusing thing for me here is... What is 'r' ? What is it the radius from? The radius from the centre? Or from the surface of the inner sphere? Or something else..??

    I fear my problem may be with the fact that I used E=V/d, which is possibly only valid for charged plates, rather than spheres? Either way, I'm still a little confused about what the 'r' actually means in the correct answer.

    Thanks for any guidance :thumbs:
  2. jcsd
  3. Mar 5, 2014 #2
    Should 'r' be defined such that:

    a < r < b

  4. Mar 6, 2014 #3


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    The expression above the ##\Delta V## formula you show is that selfsame E=Q/(4πεr2) !
    Read up on Gauss's theorem (ibidem, another two lines higher up, or Gauss's law)

    Your E=V/d is a special case for a constant ##\vec E ## all over the place.
    Otherwise (here for instance) ##\vec E = -\vec\nabla V##.

    And r is simply the distance to the center.
  5. Mar 6, 2014 #4
    Oh dear oh dear! So yeah I guess my main error was for the E=Vd part.

    I've been taught about E = -∇V before, and yeah that makes perfect sense come to think of it.

    Electric/Magnetic fields is certainly my weakest subject at the moment. Must study harder!

    Thanks for showing me that :thumbs:
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