1. Not finding help here? Sign up for a free 30min 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 due to Continuous Line Charge

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the electric field a distance z above the midpoint of a straight line segment of length
    2L, which carries a uniform line charge λ.


    2. Relevant equations
    1) my textbook says :
    E(r) = 1/4πεoV λ(r')/r2 r dl'


    2) and this also works? :
    E(r) = 1/4πεoV λ(r')/r3 r dl'

    both where r is the unit vector from the charge to the point we are caluclating the field at


    3. The attempt at a solution
    I can integrate once I get the setup down just fine. I just wanted to know when and why this two are the same. For example, in my book it says for the setup for this problem :
    E(r) = 2 * 1/4πεoV(λdx/r2)cosθz

    For one thing, how did that cos appear and since it equals z/r couldn't 2) have just been used from the start? And if 2) can be used could I apply it to surface and volume integrals?
     
  2. jcsd
  3. Dec 10, 2009 #2
    General formula for E is:

    dE = 1/4πεo (dq/r^2)[tex]\hat{r}[/tex]

    However, r = r.[tex]\hat{r}[/tex] (r_hat is unit vector)
    So you can write"

    dE = 1/4πεo (dq/r^3).r

    --
    Electric field of a point above distance Z from a line is a cumulative Electric field caused by every charge in straight line.

    Lets say an angle formed by E caused by one charge and a vertical axis is theta. From there, you can get:
    E_x = E * sin(theta)
    E_y = E * cos(theta)

    And because E in x-axis will automatically blow up, you just need to find E in y-axis.

    Hope this helps
     
  4. Dec 10, 2009 #3
    Oh now I see. I wasn't even thinking that because r_hat wasn't pointing vertically that the z component wasn't all of the electric field. I was thinking the x-fields cancelled so the field in the z direction was exactly equal to the electric field, but its actually only cos(theta) of it. Thanks a bunch
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Electric Field due to Continuous Line Charge
Loading...