Calculating Electric Field at Midpoint Between Two Charged Disks

[Puchinita5]

Homework Statement

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. What is the magnitude E of the electric field at the point on the x-axis with x coordinate a/2?
Express your answer in terms of n, R, a, and the permittivity of free space Epsilon0

Homework Equations

The Attempt at a Solution

Since I can't type this out with proper math code legibly (or at least i don't know how to), I uploaded a picture of the sheet I did my work on. Please let me know where i went wrong! I also uploaded a pic of the problem so you can visualize it. Thank you!

 

[Puchinita5]

i think that is what i did in my work??

 

[vela]

One mistake is in your calculations is that you used n as the total charge on the disk. You didn't need to do that because n is the charge density; it's what you called $\sigma$.

Also, check your integration. You didn't show any steps, so I can't tell what you did wrong.

 

[vela]

Actually, I think your integration is correct, so it's just the other mistake. Everything else looks okay to me.

 

[Puchinita5]

OOOHHH THANK YOU...yea i definitely thought n was the charge, not the charge desnity...got the answer correct when i fixed that...9 times out of 10, i usually just read the problem wrong! HAHA

thanks again! :)