# Gravitational potential of a thin ring

1. Dec 4, 2007

### DieCommie

1. The problem statement, all variables and given/known data
Consider a thin ring of radius a and mass M. A mass m is placed in the plane of the ring (not in the center!). Determine the gravitational potential for r < a. Find a position of equilibrium and determine whether it is stable or unstable. (Hint: Consider a small displacement from the equilibrium position and do an expansion.)

2. Relevant equations

3. The attempt at a solution
I drew the picture and tried to figure some sort of integral using law of cosines. I couldnt quite get any where with that though... I wonder if this is an application of Stokes' Theorem?

Any tips on which direction would be great!!
Thanks

2. Dec 5, 2007

### Gokul43201

Staff Emeritus
Some clarifications seem to be in order: What is r? Does the question want the potential due to the ring alone?

3. Dec 5, 2007

### DieCommie

I assume that r is the distance of an arbitrary point inside the ring to the center. Then a-r would be the distance from the arbitrary point to the ring. Yes, I think it wants potential due to the ring alone.