1. The problem statement, all variables and given/known data
A continuous line of charge lies along the x-axis, extending from x=+x0 to positive infinity. The line carries positive charge with a uniform linear charge density λ0.
What is the magnitude of the electric field at the origin? (Use λ0, x0 and ke as necessary.)
2. Relevant equations
1) dE = (kedq) / r2
2) dq = λdx = (Q/L)dx
3. The attempt at a solution
I used the prior equations to set up: dE = (keQ / L) * dx/x2
Now time to integrate, but first a few questions. I understand "L" is the length of the entire rod? But so is x? Am I using L and x the right way or should I put everything in terms of x? Second, what are the constants that I pull out of the integral? Since its to infinity, doesnt "L" (or x?) change, meaning I cant pull out the L? I understand ke and Q are constant so I pull them out, is that all? Also I am integrating from 0 to infinity correct? Depending on what the set integral is, I understand that there is a possibility that when I integrate, infinity might be a denominator, making that part go to 0? Im kind of confused, any help would be GREATLY appreciated!