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Finding an expression for Electric Potential?

  1. Mar 1, 2017 #1
    1. The problem statement, all variables and given/known data
    There is a thin rod with charge Q that has been bent into a semicircle with radius R. Find an expression for the electric potential at the center.

    Radius = R
    Charge = Q


    2. Relevant equations
    V = ∫(k * dq)/r


    3. The attempt at a solution
    dq = λdx
    λ = Q/L
    L = pi * r

    V = kQ / LR ∫ dx = kQ / pi * r^2 ∫ [3pi/2 - pi/2]
    V = kQ/R^2

    But the answer should be kQ/R. How did the other R get cancelled?
     
  2. jcsd
  3. Mar 1, 2017 #2

    kuruman

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    What are your limits of integration? You should use polar coordinates and integrate over an angle.
     
  4. Mar 1, 2017 #3
    I integrated from pi/2 to 3pi/2. Which came out to be just pi and that cancelled out the pi from L = pi * r.
     
  5. Mar 1, 2017 #4

    kuruman

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    Your integrand has a dx in it. What did you do with it? To integrate over an angle you need a dθ in the integrand.
     
  6. Mar 1, 2017 #5
    Oh I see. So dx should be rdθ instead for polar coordinates right, without it I can't integrate from pi/2 to 3pi/2?
     
  7. Mar 1, 2017 #6

    kuruman

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    Correct. That cancels the extra R in the denominator. Also, note that the beginning angle is arbitrary. A semicircle is a semicircle. You might as well integrate from 0 to π.
     
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