Consider two thin disks, of negligible thickness, of radius R oriented perpendicular to the x axis such that the x axis runs through the center of each disk. The disk centered at x=0 has positive charge density n, and the disk centered at x=a has negative charge density -n, where the charge density is charge per unit area.
For what value of the ratio R/a of plate radius to separation between the plates does the electric field at the point x=a/2 on the x axis differ by 1 percent from the result n/epsilon_0 for infinite sheets?
E(disk_x) = n/(2epsilon_0) * (1-((x)/(sqrt(x^2 + R^2))))
The Attempt at a Solution
I have found the electric field at x=a/2 to be:
E(disk_x) = 2*(n/(2*epsilon_0) * (1-((.5a)/(sqrt((.5a)^2 + R^2))))
However, I'm not sure where to go from here. Should I work the above equation to get what R/a is equal to and then set it equal to .99*(n/epsilon_0)?