Electric Field Intensity at a point due to a infinite line charge

[Abel I Daniel]

Homework Statement

Infinite uniform line charges of 5nc/m lie along the (positive and negative) x and y axes in free space.
Find E at :P(0,3,4)

Homework Equations

E due to line charge along the Z-axis is given by:
E=(λ/(2∏*ε*r))*ar
where λ=line charge density;ε= permitivity;r=radial distance of point from the line charge;ar=unit vector along the direction of E.

The Attempt at a Solution

Here the line charge lies in z=0 plane right??

 

[haruspex]

Here the line charge lies in z=0 plane right??

Yes. Is that all you wanted to know?

 

[rude man]

Use Gauss + superposition.

 

[Abel I Daniel]

ok,but I am trying to do without the help of Gauss law..

 

[Abel I Daniel]

so,does it require to take both the cases(along x-axis and y-axis)individually and finally add them ??
If that is the method,we will get an expression of function of x and y(instead of a constant value) right?

 

[rude man]

so,does it require to take both the cases(along x-axis and y-axis)individually and finally add them ??
If that is the method,we will get an expression of function of x and y(instead of a constant value) right?

No.
When evaluated at (0,3,4) it will be a constant. The method is immaterial to the answer.

Of course, the field at P(x0, y0, z0) is a function of z0 but not of x0 or y0.