What Is the Gravitational Field Strength Within a Uniform Thin Disk?

[tade]

I'm researching dark matter and how it affects galaxy rotation curves, I came up with the problem below.

Imagine a very thin, flat disk which has uniform mass per unit area.

What is the gravitational field strength (g) within the disk itself? How does g vary with respect to r, the distance from the center of the disk.

The area density of the disk is δ and the radius of the disk is R.

 

[A.T.]

I found this with Google, which is often better than the forum-search:

https://www.physicsforums.com/showthread.php?t=584353
https://www.physicsforums.com/showthread.php?t=39461
https://www.physicsforums.com/showthread.php?t=654136

For your case you just set the height over the disc to zero in the general formula.

 

[tade]

Most of the threads focus on the z-axis. But in order for me to simulate a galaxy, I have to focus on the x-axis.


I came up with an integral to find the value of g, but its value ends up being infinite.

I can write it down step-by-step to let you guys find out where I went wrong.