285.] POTENTIAL. I j$ 



(^) For an external point P, we might also proceed geometrically, 

 making use of the inverse point /", as in Art. 273. But we shall use the 

 analytical method. 



Just as in Art. 275, Fig. 84, we have for the mass of the ring-shaped 

 element dm = p 2 ira' 2 sin Odd, or as ap sin BdB = rdr, dm = 2 Trpardr/p^ 

 Hence the element of potential is dV = 2-jrKpadr/p, which integrated 

 between the limits from p a to / + a, gives 



M 



Hence the potential is the same as if the whole mass were concentrated 

 at the centre. 



