I have a solid cylinder of uniform charge density whose axis is centered along the z-axis. I am trying to calculate the electric field at a point on the z-axis.
What I'm trying to do is to start by first calculating the field of a disk centered on the z-axis at a point on the z-axis, then sum up a bunch of disks to find the field of the cylinder.
I find that the electric field of a uniform disk at a point on the z-axis is given by:
Where R is the radius of the disk and rho is the charge density.
Now I want to write this as:
Where z' is the position on the z-axis of the nth disk, and z-z' is the distance between the disk and the point of interest. Integrating the above expression over the length of the cylinder, however, leads to an electric field which increases with z and approaches a constant value, rather than decreasing and dropping off to zero at infinity.
I'm not sure what I'm doing wrong, but I know that I'm evaluating the above integral correctly, and I know the expression for the field of uniform disk is correct, so I must not be summing the disks properly... any help?