Two line charges lie in the XY plane

[weresquid]

Homework Statement

Line A extends from (2,2, 0) to (-2, 2, 0) and line B extends from (2, -2, 0) to (-2, -2, 0). Each has a linear charge density ρl = 1 nC / m. You want to calculate the magnitude and direction of the electric field due to the two line charges for all points on the z-axis.

a.) Sketch the charge distribution, and set up the integrals you need in order to
solve this problem. Indicate the vector R for each line charge on your plot,
and determine expressions for R and R³

b.) Prove that the magnitude of the electric field in the x and y directions is
zero.

Homework Equations

See pdf attachment.

The Attempt at a Solution

So far I've tried doing the integration technique shown in the attached pdf (this was a class example) and I am not quite sure if that's correct since there are no Z components. Also this problem is with two line charges and not one... so I guess I am basically having trouble finding out where to start? Any help is appreciated.

 

[haruspex]

What do you see as the differences between the class example and the present problem? What can you do to relate the one to the other?

 

[weresquid]

I'm guessing that I could do that formula for each line and then just sum up their total e-fields?

 

[haruspex]

I'm guessing that I could do that formula for each line and then just sum up their total e-fields?

Yes. And the other difference is? (You mentioned a concern regarding z components.)