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Help with electromagnetism

  1. Apr 22, 2003 #1
    help! I need help with this homework problem.

    --A line of positive charge is formed into a semicircle of radius R=60.0 cm. The charge per unit length along the semicircle is described by the expression [lamb]= [lamb]naught cos [the] . The total charge on the semicircle is 12.0 microcoulombs. Calculate the total force on a charge 3.00 microcoulombs at the center of curvature.--

    The figure shows the semicircle with is center at the origin going from 0 to pi. [the] is the angle formed by dragging R clockwise from the positive y axis.

    the answer in the book is -0.707Nj and I got -0.526N. Can someone please help me figure out how to properly go about solving this problem?
     
  2. jcsd
  3. Apr 22, 2003 #2


    consider the electric field at the center of the semicircle due to a little piece of the semicircle at angle θ. by symmetry, only the vertical component of this field contributes:

    dEy = - 1/4πε0 cos θ dq/r2 = - 1/4πε0 cos θ λrdθ/r2 = - 1/4πε0 cos2 θλ0dθ/r

    then integrate from π/2 to -&pi/2:

    Ey = -λ0/4πε0r∫cos2 θ dθ = -λ0/8ε0r


    the force on the charge is the Fy = qEy


    we also need to solve for λ0.

    Q = ∫dq = ∫λ0rcos θ dθ = 2rλ0

    λ0 = Q/2r

    finally
    Fy = -qQ/16ε0r2


    plug in the numbers and you get -0.70588 N.
     
  4. Apr 23, 2003 #3

    Tom Mattson

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  5. Apr 23, 2003 #4
    oops. my bad.
     
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