Uniform line charge distribution

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

Feb 2, 2014
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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:

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 $\frac{5_{ay}+4_{az}}{\sqrt{41}}$, 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