1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    gneill

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Electric field of a line of charge and direction
Loading...