Electric field from a line of charge

[midge]

Homework Statement

Positive charge q= 7.81pC is spread uniformly along a thin nonconducting rod of length L=14.5cm. What are the magnitude and direction (relative to the direction of the x axis) of the E-field produce at pt P, at distance R = 6.00 cm from the rod along its perpendicular bisector.

Homework Equations

dE= (kdQ)/r^2

The Attempt at a Solution

dQ = charge density (a) * dL --> dE = intergral from -L/2 to L/2 of (k*a*dL)/(R^2 + L^2/4)
E= k*a/ (R^2 + L^2/4) * L ---> charge density (a)= Q/L
E = kQ/(R^2 + L^2/4)

It might be a bit hard to understand all the broken notations. Sorry. I also tried to attached a diagram, please look at that to clarify. I don't think I set up the integral correctly. Help please! Thanks

 

[AUMathTutor]

Assuming the line of charge is vertical, you only need to consider the x-components of the force; the y-components will cancel out. Why? Symmetry.

Can you find an expression for the x-component of the force?

If so, just integrate that over the integration region and you'll have your answer.