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Homework Help: Electric field of a line of charge and direction

  1. Jan 1, 2013 #1
    1. The problem statement, all variables and given/known data
    A straight nonconducting plastic wire 8.50 cm long carries a charge density of +175 nC/m distributed uniformly along its length. It is lying on a horizontal table top. Find the magnitude and direction of the electric field this wire produces at a point 6.00 cm directly above its midpoint.

    2. Relevant equations
    E = [itex]\frac{1}{4πε_0}[/itex] * [itex]\frac{Q}{r^2}[/itex]
    λ = 175 nC/m
    a = 4.25 cm
    y = 6.00 cm

    3. The attempt at a solution
    I made a diagram with the rod along the x-axis, with the y-axis intersecting it at the center. The endpoints of the rod are ±a where a=4.25cm.

    dE = [itex]\frac{1}{4πε_0}[/itex] * [itex]\frac{λdx}{x^2+y^2}[/itex]
    dEy = dE sin(θ)
    sin(θ) = [itex]\frac{y}{\sqrt{x^2+y^2}}[/itex]

    dEy = [itex]\frac{λy}{4πε_0}[/itex] * [itex]\frac{dx}{(x^2+y^2)^\frac{3}{2}}[/itex]
    Ey = [itex]\frac{λy}{4πε_0}[/itex] * [itex]\int^{a}_{-a} \frac{dx}{(x^2+y^2)^\frac{3}{2}}[/itex]
    Ey = [itex]\frac{λa}{2πε_{0}y\sqrt{x^2+y^2}}[/itex]

    The result I got after plugging all the numbers in is E = 3.03 * 104 N/C but other sources online say the correct answer is 4.28 * 104 N/C. What did I do wrong?
    Last edited: Jan 1, 2013
  2. jcsd
  3. Jan 1, 2013 #2


    User Avatar

    Staff: Mentor

    I don't see a problem with what you've done. (Although you did forget to replace the 'x2' within the radical of the final line with 'a2' -- no doubt a minor oversight).

    Your answer looks okay to me.
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