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Potential different between two points in electric field

  1. Feb 3, 2014 #1
    1. The problem statement, all variables and given/known data
    If E = 6000 V/m, find the potential difference between point X and Y!
    untitled_zps75d69ec8.png
    a. 2400 V
    b. - 2400 V
    c. 6000 V
    d. - 6000 V
    e. 3000 V


    2. Relevant equations
    E = V/d

    not sure for other equations

    3. The attempt at a solution
    The electric field of X and Y will be the same. To find the potential difference, we need distance. And by distance, I think the distance should be from the electric charge to the point, but there is none.

    So, my desperate move is:
    V = E.d = 6000 x 0.5 = 3000 V , where 0.5 is the distance between X and Y?

    Am I correct? If yes, why can we use the distance between two points? Also, how to determine whether the potential difference is negative or positive?

    Thanks
     
  2. jcsd
  3. Feb 3, 2014 #2
    Vy-Vx = -∫E.dl (Note the dot product)

    Set your origin at 'X' with positive x-axis along line joining X-Y .Find the above integral with limits (0→0.5)
     
  4. Feb 3, 2014 #3
    I tried your method and I got - 3000 V as the answer. Am I wrong or there are no correct choices?

    Thanks
     
  5. Feb 3, 2014 #4

    lightgrav

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    you are wrong. dot product means only the displacement parallel the E-Field does any Work .

    and pay attention to the negative sign ... E.d = - ΔV
     
  6. Feb 3, 2014 #5
    Why are you not considering the dot product which involves an angle ?

    Vy-Vx = -∫E.dl = -∫Edlcosθ ,where θ is angle between the Electric field and the displacement . θ is constant along the path X-Y and can be easily found from the geometry of the figure .

    There is definitely a correct option given in the question.
     
  7. Feb 3, 2014 #6

    haruspex

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    It's not clear to me which way the difference is to be taken, ø(X)-ø(Y) or the reverse. Maybe you are supposed to take the unsigned difference.
     
  8. Feb 4, 2014 #7
    Oh I see my mistake. Ok I have redone the question. I suppose the value of cos θ = 4/5 ?

    If cos θ = 4/5, I got - 2400 V as final answer.

    I think the sign is important because the choices give sign potential difference.

    Thanks
     
  9. Feb 4, 2014 #8

    haruspex

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    if what is wanted is the unsigned difference then the right answer will be the positive choice.
    If what is wanted is the signed difference then I've no idea how you choose the right one. Have you quoted the question word for word?
     
  10. Feb 4, 2014 #9
    Vy - Vx = -2400V
     
  11. Feb 5, 2014 #10
    I didn't get this question from book, but from my friend. That is the question, word by word, given to me. Maybe he didn't give me the exact question from the book.

    Ok.I think I get it.



    Thanks a lot for all the help :smile:
     
  12. Feb 5, 2014 #11

    lightgrav

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    The Electric field points "electrically downhill".
    Voltages need to specify "from _x_ to _y_", or "at _y_ relative to _x_"
     
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