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Consider a uniform ring of mass and radius , centered on the origin, and lying in the  plane.
Let us consider the gravitational potential generated by such a ring in the  plane
(which corresponds to
). It follows, from Section 12.3, that for ,

(1014) 
However, , , , , and . Hence,

(1015) 
Likewise, for ,

(1016) 
giving

(1017) 
Richard Fitzpatrick
20110331