E Field due to 2 parallel oppositely charged strips

[jegues]

Homework Statement

Two parallel, very long strips are uniformly charged with charge densities $\rho_{s}$ and $- \rho_{s}$, respectively ($\rho_{s} > 0$). The cross section of the structure is shown in the figure attached. The width of the strips is the same as the distance between them (i.e. a), and the medium is air. Find the electric field intensity vector at the center of the cross section (point A).

Homework Equations

The Attempt at a Solution

See figure attached.

As the figure attached describes, I'm having trouble setting up an integral that will account for the always changing radius as we move along infinitesimily small lengths along the charged strip.

I have to describe this using one parameter, correct? How do I go about doing that?

My answer should of the form,

$\vec{E} = -2E_{1} \hat{j}$

My problem is finding $E_{1}$, due to it's ever changing radius. I know I have to use a line integral, but how do I describe is using one parameter? We should integrating along dl, correct? But we also need to describe dl in terms of the radius in order to do the line integral correct?

 

[rude man]

Think Gauss.

 

[jegues]

Think Gauss.

We haven't cover Gauss's law yet, I'm required to do it using a regular line integral.

How would I set the integral up to account for varying radii as we move along small lengths dl along the charged line?