Two line charges lie in the XY plane...

weresquid

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
See pdf attachment.

3. 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.

Attached Files

Line Charges.pdf (162.9 KB, 3 views)

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

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