A charged rod with uniform charge per length and total charge Q is placed along the z-axis with one end at the origin. The rod is located on the positive z-axis according the the diagram accompanying the problem (not shown). Find the electric field E(x,0,0) at any point along the x-axis.
1) I have been given the integral x dx / (x^2 + a^2)^3/2.
2) I have been given a second integral dx / (x^2 + a^2)^3/2
The Attempt at a Solution
Since I know I need to use those two integrals, I solved them first:
1) = - 1 / square root of (x^2 + a^2)
2) = x / a * square root of (x^2 + a^2)
I realize that the total field will be the vector sum of all the segments of the rod (and so I imagine that even though I'm solving for only the x component that it has more than just that). I believe that I need to use the equation E = ke integral of dq / r^2 unit vector r. In this, r is the distance from the charge element to a point and the unit vector r is directed "from the element toward the point." I've played around with this a bit, but I'm at a loss. I realize that I will need to use the two integrals (otherwise they wouldn't have been given in the problem), but I'm not sure where exactly I need to utilize them. I'm not sure where to go with the equation for E that I expect to need, either. Any help would be very much appreciated.