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What is the potential at point P at the center of this arc?

  1. Feb 2, 2014 #1
    1. The problem statement, all variables and given/known data

    What is the potential at point P due to a point charge Q at a distance R from P? Set V=0 at infinity. The same charge has been spread uniformly over a circular arc of radius R and central angle of 40 degrees. What is the potential at point P at the center of this arc?

    2. Relevant equations
    F=qE
    E=kq/r^2
    W=Fd
    V=W/q


    3. The attempt at a solution
    After using the equations, I got V=(kQ)/R. I think the arc would be found in a similar way, but I don't know how to take the shape into account.
     
  2. jcsd
  3. Feb 2, 2014 #2

    rude man

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    Integrate k dq/R over the 40 deg. k and R are constants. Express dq in terms of line charge density and d(theta).
     
  4. Feb 2, 2014 #3

    haruspex

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    What would be the potential from 2 charges each Q/2 and each at distance R from P? What about 3 of Q/3 each? ...
     
  5. Feb 2, 2014 #4
    Would the potential for the arc be the same as the potential of the point because potential is scalar?
     
  6. Feb 2, 2014 #5

    haruspex

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    Merely being scalar doesn't do it. Scalars can be positive or negative.
    But there are two facts you can use:
    - potentials are additive
    - the potential due to a charge depends only on the magnitude of the charge and how far away it is
     
  7. Feb 3, 2014 #6

    rude man

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    It also depends on the polarity of the charge.
     
  8. Feb 3, 2014 #7

    haruspex

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    Ok, value of the charge.
     
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