Find the flux passing through the plane

[~electric~]

Homework Statement

A linear charge pl=2.0microC/m lies on the y-z plane.from[0 -1 1] to [0 1 1]. Find the flux passing through the plane extending from 0 to 1.0m in the x-dir and -infinity to +infinity in the y direction.
***i wrote this in MATLAB and got 0.5micro as answer***

Homework Equations

Q = gauss law.
where D = pl/(2*pi*rho) , rho (distance from line to sheet).

The Attempt at a Solution

I found D = 0.32 micro C/m^2. But how do i consider the area so that i can multiply with D to get the flux ( i am assuming no integration required in this case becase the flux is perpendicular to the sheet..
Any help would be appreciated...

 

[Meir Achuz]

This is a harder problem than you think.
The D field from a finite length wilre has to be used,
not the formula you have for D.
You can't use Gauss.

 

[~electric~]

i thought i need to use Gauss' Law[(integral)D.ds] to find the flux through the entire surface.Then for finding the D for the finite wire what do i do? i am confused..

 

[~electric~]

I saw in the textbook the charge on the line can be also calculated as pL*L which gives me 4 micro C.But i don't if i use this inorder to solve the problem or not..

 

[Meir Achuz]

You have to integrate Coulomb's law for a finite length.
It is like the integral for an infinite length, but with finite limits.