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Dipole moment, electric potential

  1. Jan 29, 2017 #1
    1. The problem statement, all variables and given/known data
    I am given this picture
    upload_2017-1-29_15-56-52.png
    and I know that |q1|=2nC, |q2|=5nC, d=1mm
    I need to first find the total dipole moment of the system. Then I need to find an equation that represents the electric potential due to this net dipole moment for all (everywhere)

    2. Relevant equations
    p=qd

    3. The attempt at a solution
    I saw a formula which was p=qd (vectors)
    so I thought I would separate it into two different dipole moments, one for q1 and one for q2, and then add them together. For p1 I got 2x10^-12 in the y direction, and for p2 I got 5x10^-12 in the x direction. Would this be correct?

    Also, would I be using this formula for the potential?
    V = kpcosθ/r^2
     
    Last edited: Jan 29, 2017
  2. jcsd
  3. Jan 29, 2017 #2

    haruspex

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    What happened to the 3/2?
     
  4. Jan 29, 2017 #3
    Ok, so 7.5x10^-12 in the x direction. And for the potential?
     
  5. Jan 29, 2017 #4

    haruspex

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    Assuming a certain definition of θ, yes.
     
  6. Jan 29, 2017 #5
    I'm not quite sure what θ would be in this case
     
  7. Jan 29, 2017 #6

    haruspex

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    Maybe better to put the answer in vector form. If ##\vec p## is the dipole at the origin and ##\vec r## is a point in space, what is the potential at ##\vec r##?
     
  8. Jan 29, 2017 #7
    I don't know what the formula for potential would be,except I had V=kpcosθ/r^2 in my notes but I don't know when to use it
     
  9. Jan 29, 2017 #8

    haruspex

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    That makes for not terribly useful notes!
    It arises from the dot product of the two vectors.
     
  10. Jan 29, 2017 #9
    So the dot product of p and r?
     
  11. Jan 29, 2017 #10

    haruspex

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    Yes. Can you write the whole expression?
     
  12. Jan 29, 2017 #11
    I'm not really sure what you want, I assume r will have an x and y component, so r cosθ and r sinθ
    so then
    (7.5x10^-12)(rcosθ)+(2x10^-12)(rsinθ)

    Sorry I don't really have any idea what I am doing because I have no notes/ teaching on this stuff.
     
  13. Jan 29, 2017 #12

    haruspex

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  14. Jan 29, 2017 #13
  15. Jan 29, 2017 #14

    haruspex

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  16. Jan 29, 2017 #15
    What will the r hat be ?
     
  17. Jan 29, 2017 #16

    haruspex

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    Putting a hat on a vector is a standard notation meaning the unit vector in that direction. So for any vector ##\vec x##, ##\hat x=\frac{\vec x}{|\vec x|}##
     
  18. Jan 29, 2017 #17
    Here they don't specify a length or direction for r, it just says "everywhere"
     
  19. Jan 29, 2017 #18

    haruspex

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    The potential is necessarily a function of position. You cannot say what it is "everywhere" without involving a variable to specify position.
     
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