Force between two uniformly charged rods

[skiboka33]

I have two identical rods with length 2a with charges +Q.

Both rods are on the x axis. One is centered at (0,0) so that it ranges from (-a to a) and then other has a center at (b,0) which ranges from
(b-a to b+a). The question asks what is the force exerted by the left rod on the right rod.

Now I have an understanding of how to do these types of problems. For example if the left rod was a (0,0) point charge I would have no problem with this question.

I determined that F = k(Q^2)/4(a^2) * int[dx dx / x^2] if that is correct? Is this a double integral, and if so, what should my limits of integration be?
Is it two integrals from -a to a and b-a to b+a? Or an integral with limits b-2a to b+2a in which case i don't know what to do with the 2nd dx.

Thank you.

 

[skiboka33]

Anything would help, I don't need the problem solved for me, just some concepts cleared up. Thanks.

 

[siddharth]

What is the relation between the Electric field at a point and the force experienced by a charge at that point?
Can you see how you can apply that concept in this question?

 

[Gokul43201]

To elaborate a tad bit : Chose a point on the second rod. Find the field due to the entire first rod at this point (by integrating over the length of the first rod). Now select an element centered on this point and find the cherge on it. That tells you the force on this element. From here, find the force on the entire second rod.