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Semicircular charged wire question

  1. Jan 31, 2010 #1
    1. The problem statement, all variables and given/known data

    Charged Wire laid out in a semicircle, test charge at the center of the "Circle"
    what is the charge of dQ. This isn't my whole question but is the bit of it that I cant understand the actual question asks you to go the whole nine yards with calculating the force on the test charge

    24eddn7.jpg

    3. The attempt at a solution

    Charge density: [tex] \frac{total charge}{length of tiny wire piece}=\frac{Q}{\frac{2\pi R}{2}} = \frac{Q}{\pi R} [/tex]

    so charge of wire chunk = [itex] \frac{Q}{\pi R} * d\theta [/itex]

    when my solution manual uses the charge of the wire chunk it uses [itex] \frac{Q}{\pi R} * d\theta * R [/itex]

    I can't figure out why, any hints?
     
  2. jcsd
  3. Jan 31, 2010 #2

    Doc Al

    User Avatar

    Staff: Mentor

    The charge density is charge per unit length. The length of that wire segment is R*dθ, not just dθ.
     
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