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Potential due to uniform ring
Consider a uniform ring of mass
, radius
, and negligible crosssectional area, 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 3.4, that for
,

(3.75) 
However,
,
,
,
,
,
,
,
, and
(Abramowitz and Stegun 1965b). Hence,

(3.76) 
Likewise, for
,

(3.77) 
giving

(3.78) 
Richard Fitzpatrick
20160331