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Arc of Charge

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Electric charge of density ρℓ = 5 μC/m is distributed along the arc r = 2 cm,
    0 ≤ ∅ ≤ ∏/4, z = 0. Find the electric field intensity at (0, 0, z)

    2. Relevant equations
    dE=(dQ(r)/(4∏ε(r^2))) (unit vector R)


    3. The attempt at a solution
    Letting pL be the charge density, letting r^2 = mag(r)^3

    pLdL = dQ
    dL = rd∅
    pLrd∅ = dQ, r=0.02

    Note: Limits of integration are 0 -> ∏/4

    E(r) = 5E-6*0.02/(4∏ε)∫(z*(unitvector z) - 0.02cos∅* (unit vector x) - 0.02sin∅*(unit vector y))/((z^2+0.0004)^(3/2))) d∅

    =900∫(z*(unitvector z) - 0.02cos∅* (unit vector x) - 0.02sin∅*(unit vector y))/((z^2+0.0004)^(3/2))) d∅


    I found it kind of hard to use notation while typing, so feel free to ask me to clarify. I know what I just typed is extremely tangly, so thanks in advance for taking the time to look at it.

    My question is, did I go about this problem the right way? I don't feel confident about the evaluation I did to get all variables in terms of ∅. Also, I brought the unit vector into the calculation so that the final answer's vector will depend on whats being plugged in. I figure since z must be a constant point charge, the integral can be easily evaluated once a z value is given.
     
  2. jcsd
  3. Jan 29, 2012 #2

    SammyS

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    The result looks correct.

    You're right. It is rather hard to follow.
     
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