Uniform line charge distribution

Discussion in 'Physics' started by SilverKing, Mar 19, 2014.

  1. SilverKing

    Thread Starter Member

    Feb 2, 2014
    72
    0
    Hi everyone,

    I've the following problem, and I want to know whether my solution is right or not.

    1- Two charged line with density of 5 n c/m along the x and y axes (x±∞, y±∞), Find the Electric field at:
    (a) P(0,0,4)
    (b) P(0,5,4).

    Solution

    (a)
    Since we're dealing with an "infinite" line, we can use this formula:
    E=\frac{\rho_{l}}{2 \pi \epsilon b}, where b is the distance from the point of interest to the line.

    And since the two line have the same density and the distance to the point of interest (4 units), then:
    E=2 \frac{\ 5 \times 10^{-9}}{2 \pi \epsilon (4)}=44.95 (V/m)

    (b) I built my solution on on the following problem:

    [​IMG]

    Rzp=(1,2,3)-(0,0,3)=(1,2,0)

    I assumed that the red vector was chosen with respect to the point.

    So, depending on that, and returning to our problem:

    Ryp=(0,5,4)-(0,5,0)=(0,0,4)

    We can see that only z-component is exist, so:
    E=\frac{\ 5 \times 10^{-9}}{2 \pi \epsilon (4)}=22.47_{az} (V/m)

    Rxp=(0,5,4)-(0,0,0)=(0,5,4)
    The distance is \sqrt{41} and unit vector is [itex] \frac{5_{ay}+4_{az}}{\sqrt{41}} [/itex], so:
    E=\frac{\ 5 \times 10^{-9}}{2 \pi \epsilon \sqrt{41}} \times \frac{5_{ay}+4_{az}}{\sqrt{41} =10.95_{ay}+4.76_{az}(V/m)
     
    Last edited: Mar 19, 2014
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