What is the Electric Field at P(0,0,4)?

AI Thread Summary
To find the electric field at point P(0,0,4) due to infinite line charges of 5nC/m along the x and y axes, the relevant equation is E = (pl/2(pi)(eo)p)ap, where pl is the line charge density and ap is the unit vector. The user seeks clarification on calculating the unit vector and expresses confusion about why the answer is 45az. They propose that due to symmetry, the setup can be simplified to a single line charge with an effective density of 10nC/m at a distance of 4. Understanding the contributions from both axes and the resultant vector direction is crucial for solving the problem.
LeeroyJenkins
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Homework Statement


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


Homework Equations


E = (pl/2(pi)(eo)p)ap
pi = 3.14...
eo - permitivity of free space 8.854 x 10^-12
pl = line charge density
ap = unit vector

The Attempt at a Solution


really just need to know how to solve for the unit vector pl then I can do the rest.
I was thinking along the lines of ap = (z-4) az/ sqrt((z-4)^2) then plug in z... not really sure. Any help would be appreciated.

The answer is 45az but how?
 
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Why the unit vector pl?

Through symmetry (You're on the z-axis) isn't the set up equivalent to just a single line charge with density 10 taken from the radius of 4?
 

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